Remarks on the regularity of the minimizers of certain degenerate functionals
From MaRDI portal
Publication:1085423
DOI10.1007/BF01172492zbMath0607.49003MaRDI QIDQ1085423
Mariano Giaquinta, Giuseppe Modica
Publication date: 1986
Published in: Manuscripta Mathematica (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/155186
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Existence theories for free problems in two or more independent variables (49J10)
Related Items
Nonlinear potential theory of elliptic systems, A local estimate of the maximum of the module of the deviator of the strain tensor in an elastoplastic body with linear hardening, Higher differentiability results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions, Regularity results for local minimizers of energies with general densities having superquadratic growth, Univalent minimizers of polyconvex functionals in two dimensions, Everywhere regularity of functionals with \(\varphi \)-growth, The method of \(p\)-harmonic approximation and optimal interior partial regularity for energy minimizing \(p\)-harmonic maps under the controllable growth condition, Asymptotically regular problems I: Higher integrability, Quasiconvexity and partial regularity via nonlinear potentials, Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials, On interior regularity of minimizers of \(p(x)\)-energy functionals, On partial Hölder continuity and a Caccioppoli inequality for minimizers of asymptotically convex functionals between Riemannian manifolds, Lipschitz estimates for systems with ellipticity conditions at infinity, Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals, Examples of classically unsolvable scalar regular variational problems satisfying standard growth conditions, Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth, Global Lipschitz continuity for minima of degenerate problems, Convex functionals and partial regularity, A counterexample related to the regularity of the \(p\)-Stokes problem, Liouville-type theorems for steady flows of degenerate power law fluids in the plane, Regularity for minima of functionals with p-growth, Regularity results for vectorial minimizers of a class of degenerate convex integrals, Regularity for \(p\)-harmonic type systems with the gradients below the controllable growth, Boundary regularity for elliptic systems with \(p,q\)-growth, Global Morrey regularity for asymptotically regular elliptic equations, Lipschitz regularity for some asymptotically subquadratic problems, The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity, Global gradient bounds for the parabolicp-Laplacian system, Variational integrals on Orlicz-Sobolev spaces, An optimal gradient estimate for asymptotically regular variational integrals with multi-phase, Almost convergence in \(C^{1}\) of minimizers in regular variational problems, Harnack's estimate for a mixed local-nonlocal doubly nonlinear parabolic equation, Hölder estimates for parabolic \(p(x, t)\)-Laplacian systems, Regularity of minimizers of vectorial integrals with \(p\)-\(q\) growth, Regularity results for non-autonomous variational integrals with discontinuous coefficients, Regularity results for differential forms solving degenerate elliptic systems, Partial regularity results for quasimonotone elliptic systems with general growth, New regularity theorems for non-autonomous variational integrals with \((p,q)\)-growth, On the global \(W^{2,q}\) regularity for nonlinear \(N\)-systems of the \(p\)-Laplacian type in \(n\) space variables, Pointwise gradient estimates, Higher regularity in congested traffic dynamics, Partial regularity for minimisers of certain functionals having nonquadratic growth, Fractional differentiability results for nonlinear measure data problems with coefficients in \(C_\gamma^\alpha\), Hölder-Zygmund estimates for degenerate parabolic systems, Everywhere regularity for a class of vectorial functionals under subquadratic general growth conditions., Regularity results for a priori bounded minimizers of non-autonomous functionals with discontinuous coefficients, Partial regularity for minimizers of discontinuous quasi-convex integrals with degeneracy, On the regularity of weak solutions to the stationary motion of the degenerate power-law fluids, On local generalized minimizers and local stress tensors for variational problems with linear growth, Global Calderón-Zygmund theory for nonlinear parabolic systems, Partial regularity for manifold constrained \(p(x)\)-harmonic maps, Full \(C^{1,\alpha}\)-regularity for minimizers of integral functionals with \(L\log L\)-growth, Global regularity for almost minimizers of nonconvex variational problems, Besov regularity for a class of singular or degenerate elliptic equations, Harnack's inequality for doubly nonlinear equations of slow diffusion type, On the Hölder regularity of signed solutions to a doubly nonlinear equation, Partial regularity and potentials, Global gradient bounds for relaxed variational problems, A general low-order partial regularity theory for asymptotically convex functionals with asymptotic dependence on the minimizer, Higher integrability for minimizers of asymptotically convex integrals with discontinuous coefficients, Regularity of minima: an invitation to the dark side of the calculus of variations., On the singular set of minimizers of \(p(x)\)-energies, Regularity of minimizers of some variational integrals with discontinuity, Partial regularity of minimizers of asymptotically convex functionals with Morrey coefficients, Very degenerate elliptic equations under almost critical Sobolev regularity, Partial Hölder continuity of minimizers of functionals satisfying a VMO condition, A condition for the Hölder regularity of local minimizers of a nonlinear elastic energy in two dimensions, Interior gradient bounds for local minimizers of variational integrals under nonstandard growth conditions, A general regularity theorem for functionals with \(\varphi \)-growth, The heat flow in nonlinear Hodge theory, Partial Lipschitz regularity of minimizers of asymptotically convex functionals with general growth conditions, Local boundedness for vector valued minimizers of anisotropic functionals, Another theorem of classical solvability `in small' for one-dimensional variational problems, A regularity result for a convex functional and bounds for the singular set, Regularity results for a class of non-autonomous obstacle problems with \((p,q)\)-growth, Pointwise gradient estimates for a class of singular quasilinear equations with measure data, Variational integrals of splitting-type: higher integrability under general growth conditions, Partial regularity of solutions to \(p(x)\)-Laplacian PDEs with discontinuous coefficients, Harmonic type approximation lemmas, Local lipschitz regularity of vector valued local minimizers of variational integrals with densities depending on the modulus of the gradient, Regularity for minimizers of non-quadratic functionals: The case \(1<p<2\), Lipschitz regularity for some asymptotically convex problems, p-harmonic obstacle problems. I: Partial regularity theory, Global regularity for systems with \(p\)-structure depending on the symmetric gradient, Hölder continuity of weak solutions of \(p\)-Laplacian PDEs with VMO coefficients, Global Schauder estimates for the \(p\)-Laplace system, Gradient bounds for the horizontal \(p\)-Laplacian on a Carnot group and some applications, Partial regularity of 𝑝(𝑥)-harmonic maps, Regularity results for solutions to obstacle problems with Sobolev coefficients, Gradient Hölder regularity for degenerate parabolic systems, Global Lipschitz regularity for almost minimizers of asymptotically convex variational problems, Regularity for quasilinear vectorial elliptic systems via an iterative scheme with numerical applications, \(C^{1,\alpha}\)-solutions to non-autonomous anisotropic variational problems, Higher integrability of minimizing Young measures, Hölder continuity of local minimizers, \(L^q\)-estimates of gradients for evolutional \(p\)-Laplacian systems, Existence of a sign-changing weak solution to doubly nonlinear parabolic equations, Interior gradient regularity for \(\mathrm{BV}\) minimizers of singular variational problems, Interior integral estimates on weak solutions of certain degenerate elliptic systems, Heat flow of \(p\)-harmonic maps with values into spheres, Unnamed Item, Unnamed Item, Partial regularity of minimizers of asymptotically convex functionals with ${p(x)}$-growth, Global gradient estimates for asymptotically regular problems of p(x)-Laplacian type, On the Lipschitz Regularity for Minima of Functionals Depending on $x$, $u$, and $\nabla{u}$ under the Bounded Slope Condition, Regularity for asymptotically regular elliptic double obstacle problems of multi-phase, Regularity for double phase problems at nearly linear growth, Expansion of positivity for doubly nonlinear parabolic equations and its application, Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions, Partial regularity of minimizers for double phase functionals with variable exponents, A Local Discontinuous Galerkin Approximation for the \(\boldsymbol{{p}}\) -Navier–Stokes System, Part II: Convergence Rates for the Velocity, Boundary regularity for parabolic systems in convex domains, Regularity theory for parabolic systems with Uhlenbeck structure, On the weak Harnack estimate for nonlocal equations, Approximation of elliptic and parabolic equations with Dirichlet boundary conditions, Geometric linearisation for optimal transport with strongly \(p\)-convex cost, On Quasi-static Non=Newtonian Fluids with Power-law, Global Morrey regularity results for asymptotically convex variational problems, Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems, Partial regularity results for asymptotic quasiconvex functionals with general growth, Existence and regularity of minimizers of nonconvex integrals withp-qgrowth, Variational integrals with a wide range of anisotropy, Everywhere regularity for vectorial functionals with general growth, Lipschitz regularity of solutions of some asymptotically convex problems, Unnamed Item, Interior behaviour of minimizers for certain functionals with nonstandard growth, Unnamed Item, Unnamed Item, Regulaity for minimizers of certain degenerate functionals with non-standard growth conditions, On the hausdorff dimension of the singular set of stable-stationary harmonic maps, The regularity of general parabolic systems with degenerate diffusion, Partial regularity of minimizers of p (x )-growth functionals with 1 < p (x ) < 2, ENERGY CONCENTRATION PROPERTIES OF A p-GINZBURG–LANDAU MODEL
Cites Work
- Unnamed Item
- Regularity of minimizing harmonic maps into the sphere
- Differentiability of minima of non-differentiable functionals
- \(C^{1,\alpha}\) partial regularity of functions minimising quasiconvex integrals
- Partial regularity of minimizers of quasiconvex integrals
- Partial regularity for minima of variational integrals
- On the regularity of the minima of variational integrals
- Regularity for a class of nonlinear elliptic systems
- Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
- On Harnack's theorem for elliptic differential equations
- Elliptic Partial Differential Equations of Second Order
