Regularity for a more general class of quasilinear equations

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DOI10.1016/0022-0396(84)90105-0zbMath0488.35017OpenAlexW1977355332MaRDI QIDQ1166015

Peter Tolksdorf

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(84)90105-0

zbMATH Keywords

Caratheodory-function Euler-equations interior-regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Nonlinear higher-order PDEs (35G20)

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equations in convex cones, Extremals for the singular Moser-Trudinger inequality via n-harmonic transplantation, Homogenization in Sobolev spaces with nonstandard growth: brief review of methods and applications, Eigenvalue estimate for the weighted \(p\)-Laplacian, Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions, Level-set inequalities on fractional maximal distribution functions and applications to regularity theory, Epsilon-regularity for \(p\)-harmonic maps at a free boundary on a sphere, Qualitative properties of bounded subsolutions of nonlinear PDEs, Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems, Principal eigenvalue in an unbounded domain with indefinite potential, Positive maximal and minimal solutions for non-homogeneous elliptic equations depending on the gradient, \(p\)-harmonic maps to \(S^1\) and stationary varifolds of codimension two, Existence of positive solutions for an elliptic system involving nonlocal operator, Sharp weighted Trudinger-Moser inequalities with the \(L^n\) norm in the entire space \(\mathbb{R}^n\) and existence of their extremal functions, Local Lipschitz bounds for solutions to certain singular elliptic equations involving the one-Laplacian, \(C^{1, \alpha}\)-regularity for variational problems in the Heisenberg group, On local Lipschitz regularity for quasilinear equations in the Heisenberg group, Anisotropic \(p\)-Laplacian evolution of fast diffusion type, On the Morse index of least energy nodal solutions for quasilinear elliptic problems, On the \(p\)-Laplacian Lichnerowicz equation on compact Riemannian manifolds, Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data, Liouville results for \(m\)-Laplace equations in half-space and strips with mixed boundary value conditions and finite Morse index, Improved Moser-Trudinger inequality of Tintarev type in dimension \(n\) and the existence of its extremal functions, Maximum and comparison principles for degenerate elliptic systems and some applications, Sharp pointwise estimates for weighted critical \(p\)-Laplace equations, Liouville theorems for nonlinear elliptic equations on Riemannian manifolds, Infinitely many sign-changing solutions for \(p\)-Laplacian equation involving the critical Sobolev exponent, The Pohozaev identity for the anisotropic \(p\)-Laplacian and estimates of the torsion function, Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations, The first eigenvalue of Finsler \(p\)-Laplacian, Symmetry results for nonlinear elliptic operators with unbounded drift, Positive and sign-changing solutions of a Schrödinger-Poisson system involving a critical nonlinearity, Principal eigenvalue of \(p\)-Laplacian operator in exterior domain, Factorization into \(k\)-bubbles for Palais-Smale maps to potential type energy functionals, Nonlinear extensions of the Perron-Frobenius theorem and the Krein-Rutman theorem, Positive solutions for a singular and superlinear \(p\)-Laplacian problem with gradient term, A-priori bounds for quasilinear problems in critical dimension, Liouville type theorems for stable solutions of \(p\)-Laplace equation in \(\mathbb{R}^N\), A proof of the \(C^{p^\prime}\)-regularity conjecture in the plane, Ground states for nonlinear Kirchhoff equations with critical growth, Remarks on the existence of solutions to some quasilinear elliptic problems involving the Hardy-Leray potential, Regularity of the extremal solution for singular \(p\)-Laplace equations, Superposition operators between Sobolev spaces and a non-existence result of higher-order regular solutions for the \(p\)-Laplacian, Ground state solutions for quasilinear scalar field equations arising in nonlinear optics, Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems, From affine Poincaré inequalities to affine spectral inequalities, Lions-type theorem of the \(p\)-Laplacian and applications, Normalized solutions of nonautonomous Kirchhoff equations: sub- and super-critical cases, Isolated singularities for the \(n\)-Liouville equation, Sharp lower bound for the first eigenvalue of the weighted \(p\)-Laplacian. I, Ground state solution of critical Schrödinger equation with singular potential, Soliton solutions for quasilinear Schrödinger equations involving convolution and critical Nonlinearities, Singular Moser-Trudinger inequality involving \(L^n\) norm in the entire Euclidean space, Inverse problem related to boundary shape identification for a hyperbolic differential equation, Global Schauder estimates for the \(p\)-Laplace system, Symmetry for positive critical points of Caffarelli-Kohn-Nirenberg inequalities, On nonhomogeneous elliptic equations with the Hardy-Leray potentials, \(p\)-Laplacian diffusion coupled to logistic reaction: asymptotic behavior as \(p\) goes to 1. To the memory of Professor Ireneo Peral Alonso, a brilliant mathematician, excellent person and dear friend, Global second order Sobolev-regularity of \(p\)-harmonic functions, Optimal regularity of stable solutions to nonlinear equations involving the \(p\)-Laplacian, Nonexistence of positive solutions for high-order Hardy-Hénon systems on \(\mathbb{R}^n\), Hilbert's 19th problem revisited, Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence, Local Hölder regularity for the general non-homogeneous parabolic equations, On subhomogeneous indefinite \(p\)-Laplace equations in the supercritical spectral interval, On the generalised Brézis-Nirenberg problem, A priori bounds and existence of non-negative solutions to a quasi-linear Schrödinger equation involving \(p\)-Laplacian, Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities, An existence result for anisotropic quasilinear problems, Positive ground state solutions for the Chern-Simons-Schrödinger system, Multiple solutions of a quasilinear elliptic problem involving nonlinear boundary condition on exterior domain, Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds, Unnamed Item, Nonlinear eigenvalue problems for quasilinear equations in unbounded domains, On the Cheeger–Buser Type Inequalities for the p-Laplacian, Prescribed singular submanifolds of some quasilinear elliptic equations, Asymptotics of Sobolev embeddings and singular perturbations for the 𝑝-Laplacian, Stability results for some nonlinear elliptic equations involving thep-Laplacian with critical Sobolev growth, Unnamed Item, Smooth regularity of solutions of double obstacle problems involving degenerate elliptic equations, A further remark on the regularity of the solutions of the p-Laplacian and its applications to their finite element approximation, Semiclassical states of p-Laplacian equations with a general nonlinearity in critical case, A note on the boundary regularity of solutions to quasilinear elliptic equations, Schrödinger-Poisson equations in R^3 involving critical Sobolev exponents, Quasilinear problems with exponential growth in the reaction term, Regular positive solutions to p-Laplacian systems on unbounded domain, A note on a nonresonance condition for a quasilinear elliptic problem, Quasilinear elliptic equations involving critical Sobolev exponents, On multiplicity of positive solutions forN-Laplacian with singular and critical nonlinearity, Boundedness and blow-up of solutions for a nonlinear elliptic system, Existence of positive solutions for nonlinear Kirchhoff type problems in R3 with critical Sobolev exponent, Regularity and comparison principles for p-Laplace equations with vanishing source term, Remarks on uniqueness results of the first eigenvalue of the p-Laplacian, Existence and Approximation for Variational Problems Under Uniform Constraints on the Gradient by Power Penalty, Rigidity properties of smooth metric measure spaces via the weighted 𝑝-Laplacian, Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems, On an Emden-Fowler type equation, Unnamed Item, Existence and regularity for a general class of quasilinear elliptic problems involving the Hardy potential, Everywhere Hölder continuity of vectorial local minimizers of special classes of integral functionals with rank one integrands, Pointwise a priori estimates for solutions to some \(p\)-Laplacian equations, Pohozaev identity for Finsler anisotropic problems, On an estimate for solutions of nonlinear elliptic variational inequalities, An averaged space-time discretization of the stochastic \(p\)-Laplace system, Regularity for local minima of a special class of vectorial problems with fully anisotropic growth, \(C^{1, \alpha}\)-regularity of quasilinear equations on the Heisenberg group, Solutions fortes et majorations asymptotiques pour le modèle de Darcy Forchheimer en convection naturelle, A Liouville theorem for weightedp−Laplace operator on smooth metric measure spaces, On a free boundary problem for a class of anisotropic equations, A multiplicity results for a singular equation involving thep(x)-Laplace operator, Positive solutions for the p-Laplacian: application of the fibrering method, An existence theorem for nonlinear hemivariational inequalities at resonance, Wulff shape characterizations in overdetermined anisotropic elliptic problems, Strict convexity and the regularity of solutions to variational problems, Standing waves of modified Schrödinger equations coupled with the Chern–Simons gauge theory, Optimal C1,α estimates for a class of elliptic quasilinear equations, On extremals for the Trudinger-Moser inequality with vanishing weight in the N-dimensional unit ball, Existence and nonexistence in a class of equations with supercritical growth, A Stability Result for Extremal Functions for Some Sharp Sobolev Inequalities with Critical Exponent, Fractional differentiability for solutions of the inhomogeneous 𝑝-Laplace system, Unnamed Item, Unnamed Item, Existence of positive solutions for some problems with nonlinear diffusion, The game theoreticp-Laplacian and semi-supervised learning with few labels, Solutions of quasilinear elliptic equations in R^N decaying at infinity to a non-negative number, Principal eigenvalue of the p-laplacian in RN, Global bifurcation for quasilinear elliptic equations, The behaviour, of stationary solutions to some nonlinear diffusion problems, Boundary regularity for solutions of degenerate elliptic equations, On some nonlinear equations involving the_p-laplacian with critical sobolev growth and perturbation terms, Boundedness of the first eigenvalue of the 𝑝-Laplacian, Eigenvalue problems for quasilinear elliptic equations on R^N, Existence of Multiple Positive Solutions for N-Laplacian in a Bounded Domain in ℝ^N, Uniqueness of positive solutions for singular problems involving the $p$-Laplacian, An optimization problem for the first weighted eigenvalue problem plus a potential, Unnamed Item, On the Free Boundary in Heterogeneous Obstacle-Type Problems with Two Phases, NODAL SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS, Singular limit of quasilinear Neumann problems, On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case, A Variational Method for Second Order Shape Derivatives, Steiner symmetry in the minimization of the first eigenvalue in problems involving the 𝑝-Laplacian, Optimization of the first eigenvalue in problems involving the 𝑝-Laplacian, MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH A DISCONTINUOUS NONLINEARITY, $1$D symmetry for solutions of semilinear and quasilinear elliptic equations, A Regularity Result for the p-Laplacian Near Uniform Ellipticity, Regulaity for minimizers of certain degenerate functionals with non-standard growth conditions, Positive solutions of indefinite equations withp-Laplacian and supercritical nonlinearity, A Local estimate for nonlinear equations with discontinuous coefficients, Hardy inequalities with optimal constants and remainder terms, Sufficient conditions for the existence and asymptotic behaviour of solution to a quasi-linear elliptic problem, Entropy solutions for the $p(x)$-Laplace equation, A priori estimates for a class of quasi-linear elliptic equations, A Remark on an Overdetermined Problem in Riemannian Geometry, Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle, On the structure of spatial infinity. I. The Geroch structure, Unnamed Item, PROFILE OF SOLUTIONS WITH SHARP LAYERS TO SOME SINGULARLY PERTURBED QUASILINEAR DIRICHLET PROBLEMS, Théorèmes de régularité locale pour des systèmes elliptiques dégénérés et des problèmes non différentiables, On The Dirichletproblem for Quasilinear Equations, On the equivalence of stochastic completeness and Liouville and Khas’minskii conditions in linear and nonlinear settings, Boundary case of equality in optimal Loewner-type inequalities, Regularity properties for p−dead core problems and their asymptotic limit as p→∞, Nonexistence of Solutions and an Anti-Maximum Principle for Cooperative Systems with thep-Laplacian, Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth, SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS, Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents, Degenerate quasilinear elliptic equations arising from bimaterial problems in elastic–plastic mechanics11The financial support of the author by the EPSRC under grant GR/J37737 is gratefully acknowledged., ASYMPTOTIC BEHAVIOUR OF MINIMIZING SEQUENCES FOR HARDY'S INEQUALITY, On the resonant Lane–Emden problem for the p-Laplacian, The isolation of the first eigenvalue for a Dirichlet eigenvalue problem involving the Finsler $p$-Laplacian and a nonlocal term, Explosive solutions of quasilinear elliptic equations: existence and uniqueness, Quasilinear elliptic problems with critical exponents, Some remarks on Liouville type results for quasilinear elliptic equations, Compactness of extremals for singular Trudinger-Moser inequalities on the whole Euclidean space, Positive solutions to superlinear semipositone problems on the exterior of a ball, Boundary Singularities ofN-Harmonic Functions, A strong comparison principle for the $p$-Laplacian, Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature, Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities, On a class of sublinear quasilinear elliptic problems, A rearrangement minimization problem corresponding top-Laplacian equation, On the local Hölder continuity of the inverse of the $p$-Laplace operator, Multiple nontrivial solutions for nonlinear eigenvalue problems, Existence and multiplicity results for quasilinear elliptic equations, On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds, A regularity result via fractional maximal operators for p-Laplace equations in weighted Lorentz spaces, Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries, Study of a second-order nonlinear elliptic problem generated by a divergence type operator on a compact Riemannian manifold, Global existence and multiplicity for nonlinear Robin eigenvalue problems, Existence and boundary asymptotic behavior of strictly convex solutions for singular Monge-Ampère problems with gradient terms, Uniqueness of bounded solutions to \(p\)-Laplace problems in strips, Multiple solutions for perturbed quasilinear elliptic problems, Ground state solution for quasi-linear elliptic systems with general source terms on unbounded domain, Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds, On the local everywhere Hölder continuity for weak solutions of a class of not convex vectorial problems of the calculus of variations, Extremal parameter for double phase problem with concave-convex nonlinearity, Interior regularity results for inhomogeneous anisotropic quasilinear equations, Spectral optimization for weighted anisotropic problems with Robin conditions, The quasi-linear Brezis-Nirenberg problem in low dimensions, Symmetry via the moving plane method for a class of quasilinear elliptic problems involving the Hardy potential, Regularity results for Choquard equations involving fractional p‐Laplacian, Gibbons' conjecture for quasilinear elliptic equations involving a gradient term, Strong comparison and strong maximum principles for quasilinear elliptic equations with a gradient term, Gradient walks and $p$-harmonic functions, On the uniform vanishing property at infinity of \(W^{s, p}\)-sequences, On a degenerate singular elliptic problem, Nonhomogeneous equations with critical exponential growth and lack of compactness, Bang-Bang and Multiple Valued Optimal Solutions of Control Problems Related to Quasi-linear Elliptic Equations, Gradient continuity estimates for the normalized p-Poisson equation, W1,p(⋅) regularity for quasilinear problems with irregular obstacles on Reifenberg domains, A note on radiality of solutions of P-laplacian, Liouville‐type results for a class of quasilinear elliptic systems and applications, Extremal functions for the Moser–Trudinger inequality of Adimurthi–Druet type in W1,N(ℝN), Nonexistence of solutions to a quasilinear elliptic problem, Bifurcation problems for the 𝑝-Laplacian in 𝑅ⁿ, Existence and concentration of ground state solution to a nonlocal Schrödinger equation, On global instability of solutions to hyperbolic equations with non-Lipschitz nonlinearity, Monotonicity of Positive Solutions to − Δp u + a(u)|∇u|q = f(u) in the Half-Plane in the Case $$p\leqslant 2$$, Rayleigh quotients of the level set manifolds related to the nonlinear PDE, On some quasilinear equations involving the p-Laplacian with Robin boundary conditions, EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR DEGENERATE HEMIVARIATIONAL INEQUALITIES INVOLVING LERAY–LIONS TYPE OPERATOR WITH CRITICAL GROWTH, On the gravitational potential of modified Newtonian dynamics, Critical groups and multiple solutions for Kirchhoff type equations with critical exponents, Entire solutions of quasilinear elliptic equations, QUASILINEAR PROBLEMS WITH THE COMPETITION BETWEEN CONVEX AND CONCAVE NONLINEARITIES AND VARIABLE POTENTIALS, Positive solutions for a class of elliptic equations, Uniqueness to quasilinear problems for the \(p\)-Laplacian in radially symmetric domains, Asymptotically linear Dirichlet problem for the \(p\)-Laplacian, Weak solutions for singular quasilinear elliptic systems, Some Liouville-type Theorems for the Stationary Ginsburg – Landau Equation on Quasi-model Riemannian Manifolds, Regularity and Morse Index of the Solutions to Critical Quasilinear Elliptic Systems, Unnamed Item, Regularity of the solution of Darcy-Forchheimer's equation, Nonexistence results and estimates for some nonlinear elliptic problems, On the continuity of the free boundary in the problemΔ_pu = − (h(x, y)χ(u))_x, On Limits Of Solutions of Quasilinear Equations With Nearly Critical Exponents, Optimal constants in the exceptional case of Sobolev inequalities on Riemannian manifolds, Unnamed Item, Second order regularity for the p (x )-Laplace operator, Brunn-Minkowski inequalities for two functionals involving thep-Laplace operator, Unnamed Item, Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations, Unnamed Item, On a Bernoulli-type overdetermined free boundary problem, Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound, Gradient estimates for nonlinear elliptic equations with a gradient-dependent nonlinearity, The pseudo-p-Laplace eigenvalue problem and viscosity solutions asp→ ∞, Unnamed Item, A remark on an improved Trudinger–Moser inequality in high dimensions, Regularity of stable solutions to quasilinear elliptic equations on Riemannian models, The Ambrosetti–Prodi Problem for thep-Laplace Operator, On some aspects of oscillation theory and geometry, Radial symmetry forp-harmonic functions in exterior and punctured domains, Quasilinear Scalar Field Equations Involving Critical Sobolev Exponents and Potentials Vanishing at Infinity, Estimates and asymptotic expansions for condenser p-capacities. The anisotropic case of segments, Fractional thoughts, Existence results and a priori estimates for solutions of quasilinear problems with gradient terms, Analysis of weighted p-harmonic forms and applications, On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations, Monotonicity results in half-spaces for thep-Laplacian, On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded, On nonexistence of positive solutions of quasi-linear inequality on Riemannian manifolds, Multiplicity of solution for a quasilinear equation with singular nonlinearity, Regularity of Inhomogeneous Quasi-Linear Equations on the Heisenberg Group, Symmetry results for stable and monotone solutions to fibered systems of PDEs, Existence of multiple solutions for a singular and quasilinear equation, The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity, Improved regularity for the p-Poisson equation, Note on an elementary inequality and its application to the regularity of p-harmonic functions, Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions, A second-order Sobolev regularity for \(p(x)\)-Laplace equations, Improved Friedrichs inequality for a subhomogeneous embedding, Unified approach to \(C^{1, \alpha}\) regularity for quasilinear parabolic equations, Higher differentiability and existence for a class of problems under \(p, q\) subquadratic growth, Borderline gradient continuity for the normalized \(p\)-parabolic operator, An improved Trudinger-Moser inequality involving \(N\)-Finsler-Laplacian and \(L^p\) norm, Regularity for $p$-Harmonic Functions in the Grušin Plane, A quantitative second order estimate for (weighted) \(p\)-harmonic functions in manifolds under curvature-dimension condition, Extremal Functions for an Improved Trudinger-Moser Inequality Involving $L^p$-Norm in $\mathbb{R}^n$, Calderón–Zygmund theory for asymptotically regular nonlinear elliptic problems with double obstacles, The best constant for 𝐿^{∞}-type Gagliardo-Nirenberg inequalities, Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations, Normalized ground states to the \(p\)-Laplacian equation with general nonlinearities, A sharp Moser-Trudinger type inequality involving \(L^p\) norm in \(\mathbb{R}^n\) with degenerate potential, Local and global properties of \(p\)-Laplace Hénon equation, Sufficient and necessary conditions on the existence and estimates of boundary blow-up solutions for singular \(p\)-Laplacian equations, Schrödinger equations with Stein-Weiss type nonlinearity and potential vanishing at infinity, Reverse Faber-Krahn inequality for the \(p\)-Laplacian in hyperbolic space, A nonsmooth variational approach to semipositone quasilinear problems in \(\mathbb{R}^N\), Regularity and Pohozaev identity for the Choquard equation involving the \(p\)-Laplacian operator, Classification of positive solutions to \(p\)-Laplace equations with critical Hardy-Sobolev exponent, Stable solutions to double phase problems involving a nonlocal term, Interior pointwise gradient estimates for quasilinear elliptic equations in Heisenberg group, Anisotropic Moser-Trudinger inequality involving \(L^n\) norm in the entire space \(\mathbb{R}^n\), Uniqueness and Stability in an Inverse Problem for Electromagnetic Forming of a Metal Jet, Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators, A weak solution to a perturbed one-Laplace system by \(p\)-Laplacian is continuously differentiable, First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow, The multiplicity of solutions for the critical problem involving the fracional p-Laplacian operator

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