Overview of differential equations with non-standard growth
From MaRDI portal
Publication:972408
DOI10.1016/j.na.2010.02.033zbMath1188.35072OpenAlexW1974639734MaRDI QIDQ972408
Út V. Lê, Petteri Harjulehto, Matti Nuortio, Peter A. Hästö
Publication date: 25 May 2010
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.na.2010.02.033
regularityexistenceuniquenesseigenvalue problemelliptic equationsharmonic functionsparabolic equationsvariable exponentnon-standard growth
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)
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Cites Work
- The fundamental convergence theorem for \(p(\cdot )\)-superharmonic functions
- Degenerate parabolic equations
- A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
- Infinitely many non-negative solutions for a Dirichlet problem involving \(p(x)\)-Laplacian
- Orlicz spaces and modular spaces
- Quasi-minima
- Strong solutions for generalized Newtonian fluids
- Infinitely many positive solutions for a \(p(x)\)-Kirchhoff-type equation
- On a non-homogeneous eigenvalue problem involving a potential: an Orlicz-Sobolev space setting
- The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values
- On the existence and stability of solutions for Dirichlet problem with \(p(x)\)-Laplacian
- On stationary thermo-rheological viscous flows
- Existence and asymptotic behavior of blow-up solutions to a class of \(p(x)\)-Laplacian problems
- Retracted: Nonlinear eigenvalue problems in Sobolev spaces with variable exponent
- Global \(C^{1,\alpha}\) regularity for variable exponent elliptic equations in divergence form
- Existence of positive solutions for elliptic systems with nonstandard \(p(x)\)-growth conditions via sub-supersolution method
- Harnack's inequality for quasiminimizers with nonstandard growth conditions
- Partial regularity for minima of higher order functionals with \(p(x)\)-growth
- Regularity for minimizers of functionals with nonstandard growth by \(\mathcal A\)-harmonic approximation
- Elliptic equations with nonstandard growth involving measures
- Regularity results for a class of obstacle problems under nonstandard growth conditions
- Existence of solution for a degenerate \(p(x)\)-Laplacian equation in \(\mathbb R^N\)
- On some quasilinear elliptic equations with critical Sobolev exponents and
- The obstacle problem for nonlinear elliptic equations with variable growth and \(L^{1}\)-data
- Boundary blow-up solutions to \(p(x)\)-Laplacian equations with exponential nonlinearities
- Harnack estimates for quasi-linear degenerate parabolic differential equations
- On an open problem involving the \(p(x)\)-Laplacian-A further study on the multiplicity of weak solutions to \(p(x)\)-Laplacian equations
- Existence of solutions for \(p(x)\)-Laplacian equations with singular coefficients in \(\mathbb R^N\)
- Existence of solutions for a class of elliptic systems in \(\mathbb R^{N}\) involving the \((p(x),q(x))\)-Laplacian
- Perturbation for a \(p(x)\)-Laplacian equation involving oscillating nonlinearities in \(R^N\)
- Regularity of minima: an invitation to the dark side of the calculus of variations.
- Boundary asymptotic and uniqueness of solution for a problem with \(p(x)\)-Laplacian
- Existence of positive solutions for \(p(x)\)-Laplacian equations in unbounded domains
- A constrained minimization problem involving the \(p(x)\)-Laplacian in \(\mathbb R^N\)
- Global nonexistence for nonlinear Kirchhoff systems
- A multiplicity result for \(p(x)\)-Laplacian problem in \(\mathbb R^N\)
- New diffusion models in image processing
- Existence of multiple solutions for weighted \(p(r)\)-Laplacian equation Dirichlet problems
- Remarks on eigenvalue problems involving the \(p(x)\)-Laplacian
- Asymptotic stability for anisotropic Kirchhoff systems
- Harnack's inequality for \( p(\cdot\))-harmonic functions with unbounded exponent \(p\)
- On the boundary blow-up solutions of \(p(x)\)-Laplacian equations with singular coefficient
- Maximum principles for anisotropic elliptic inequalities
- Multiplicity of positive solutions for a class of inhomogeneous Neumann problems involving the \(p(x)\)-Laplacian
- A local mountain pass theorem and applications to a double perturbed \(p(x)\)-Laplacian equations
- Infinitely many solutions for a hemivariational inequality involving the \(p(x)\)-Laplacian
- Existence of three solutions for a class of quasilinear elliptic systems involving the \((p(x),q(x))\)-Laplacian
- On the \(C^{1,\gamma}(\overline \varOmega)\cap W^{2,2}(\varOmega) \) regularity for a class of electro-rheological fluids
- Elliptic boundary value problems with nonstandard growth conditions
- Blow-up for parabolic and hyperbolic problems with variable exponents
- Infinitely many solutions for a \(p(x)\)-Laplacian equation in \(\mathbb R^N\)
- Very weak solutions of higher-order degenerate parabolic systems
- Existence of solutions for weighted \(p(r)\)-Laplacian impulsive system periodic-like boundary value problems
- Existence of solutions and nonnegative solutions for weighted \(p(r)\)-Laplacian impulsive system multi-point boundary value problems
- Boundedness of solutions for an elliptic equation with non-standard growth
- The principle of concentration compactness in \(L^{p(x)}\) spaces and its application
- Large solutions for the Laplacian with a power nonlinearity given by a variable exponent
- Infinitely many periodic solutions for variable exponent systems
- \(p(x)\)-harmonic functions with unbounded exponent in a subdomain
- The behaviour of the \(p(x)\)-Laplacian eigenvalue problem as \(p(x)\rightarrow \infty \)
- A free boundary problem for the \(p(x)\)-Laplacian
- Limits as \(p(x)\rightarrow \infty \) of \(p(x)\)-harmonic functions
- On the regularity of the minima of variational integrals
- On Lavrentiev's phenomenon
- On some variational problems
- Hölder continuity of minimizers of functionals with variable growth exponent
- A Knobloch-type result for \(p(t\))-Laplacian systems.
- Regularity results for parabolic systems related to a class of non-Newtonian fluids.
- The Dirichlet energy integral on intervals in variable exponent Sobolev spaces
- Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
- Existence results to elliptic systems with nonstandard growth conditions
- Regularity results for stationary electro-rheological fluids
- Hartman-type results for \(p(t)\)-Laplacian systems
- Very weak solutions of parabolic systems of \(p\)-Laplacian type
- Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
- Existence and multiplicity of solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
- The quasi-minimizer of integral functionals with \(m(x)\) growth conditions
- Existence of solutions for a \(p(x)\)-Kirchhoff-type equation
- Existence of positive solutions for a class of \(p(x)\)-Laplacian systems
- Nodal solutions of \(p(x)\)-Laplacian equations
- Eigenvalues of the \(p(x)\)-Laplacian Neumann problems
- Remarks on Ricceri's variational principle and applications to the \(p(x)\)-Laplacian equations
- An obstacle problem and superharmonic functions with nonstandard growth
- On a Dirichlet problem with \(p(x)\)-Laplacian
- \(p(x)\)-Laplacian equations satisfying Cerami condition
- Graduated adaptive image denoising: Local compromise between total variation and isotropic diffusion
- Calderón-Zygmund estimates for higher order systems with \(p(x)\) growth
- Eigenvalues of the \(p(x)\)-Laplacian Steklov problem
- Compact embedding from \(W_0^{1,2}(\Omega)\) to \(L^{q(x)}(\Omega )\) and its application to nonlinear elliptic boundary value problem with variable critical exponent
- Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent
- The method of intrinsic scaling. A systematic approach to regularity for degenerate and singular PDEs
- Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in \(\mathbb R^N\)
- \(C^{1,\alpha}\)-regularity for electrorheological fluids in two dimensions
- Oscillatory property of solutions for \(p(t)\)-Laplacian equations
- Existence and asymptotic behavior of positive solutions to \(p(x)\)-Laplacian equations with singular nonlinearities
- Unbounded supersolutions of nonlinear equations with nonstandard growth
- Solutions for Neumann boundary value problems involving \(p(x)\)-Laplace operators
- \(p(x)\)-Laplacian equations in \(\mathbb R^N\) with periodic data and nonperiodic perturbations
- Existence of three solutions for \(p(x)\)-Laplacian equations
- Minimizers of the variable exponent, non-uniformly convex Dirichlet energy
- Continuous spectrum for a class of nonhomogeneous differential operators
- Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
- Elliptic equations and systems with nonstandard growth conditions: existence, uniqueness and localization properties of solutions
- Regularity of quasi-minimizers of integral functionals with discontinuous \(p(x)\)-growth conditions
- Higher integrability for parabolic equations of \(p(x,t)\)-Laplacian type
- Hölder continuity of weak solutions for parabolic equations with nonstandard growh conditions
- Renormalized solutions for nonlinear elliptic equations with variable exponents and \(L^1\) data
- Existence of periodic solutions for \(p(t)\)-Laplacian systems
- Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems
- Calderón-Zygmund type estimates for a class of obstacle problems with \(p(x)\) growth
- Higher integrability of very weak solutions of systems of \(p(x)\)-Laplacean type
- Regularity and existence of solutions of elliptic equations with p,q- growth conditions
- Wolff potential estimates for elliptic equations with nonstandard growth and applications
- A Hölder continuity result for a class of obstacle problems under non standard growth conditions
- Global regularity and stability of solutions to elliptic equations with nonstandard growth
- Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian
- Elliptic problems in variable exponent spaces
- Intrinsic scaling for PDEs with an exponential nonlinearity
- EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS
- Form estimates for the 𝑝(𝑥)-Laplacean
- A MULTIPLICITY THEOREM FOR A VARIABLE EXPONENT DIRICHLET PROBLEM
- EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A NEUMANN PROBLEM INVOLVING VARIABLE EXPONENT GROWTH CONDITIONS
- On the stability of solutions for thep(x)-Laplacian equation and some applications to optimisation problems with state constraints
- "Mappings of Finite Distortion and PDE with Nonstandard Growth"
- Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent
- Variable exponent Sobolev spaces with zero boundary values
- On a class of nonlinear problems involving a p(x)-Laplace type operator
- Entropy solutions for the $p(x)$-Laplace equation
- Singular solutions of elliptic equations with nonstandard growth
- AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
- Hölder continuity of the gradient of p(x)-harmonic mappings
- A class of De Giorgi type and Hölder continuity
- On very weak solutions of certain elliptic systems
- Weak minima of variational integrals.
- Integral representation and Γ-convergence of variational integrals withp(x)-growth
- Calderón-Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics
- The existence of solutions for elliptic systems with nonuniform growth
- On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
- Regularity of nonstandard lagrangians ƒ(x, ξ)
- The regularity of Lagrangiansf(x, ξ)=254-01254-01254-01with Hölder exponents α(x)
- On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent
- On a Dirichlet Problem with Generalizedp(x)-Laplacian and Some Applications
- Gradient estimates for thep(x)-Laplacean system
- Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition
- Variable Exponent, Linear Growth Functionals in Image Restoration
- Hölder continuity of $ p(x)$-harmonic functions
- Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator
- A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
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