Global regularity and stability of solutions to elliptic equations with nonstandard growth

DOI10.1080/17476930903568399zbMath1232.35030OpenAlexW2125962027WikidataQ110099031 ScholiaQ110099031MaRDI QIDQ3093060

Petteri Harjulehto, Michela Eleuteri, Teemu Lukkari

Publication date: 12 October 2011

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930903568399

zbMATH Keywords

Hardy inequalityboundary regularityglobal higher integrabilityglobal reverse Hölder inequality,Sobolev-Poincard inequality

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Stability in context of PDEs (35B35) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Perturbations in context of PDEs (35B20)

Related Items (7)

The stability of parabolic problems with nonstandard \(p(x,t)\)-growth ⋮ Global \(L^\infty\)-estimates and Hölder continuity of weak solutions to elliptic equations with the general nonstandard growth conditions ⋮ Global regularity and stability of solutions to obstacle problems with nonstandard growth ⋮ Stability of solutions to obstacle problems with generalized Orlicz growth ⋮ Sharp gradient estimates for quasilinear elliptic equations with \(p(x)\) growth on nonsmooth domains ⋮ Overview of differential equations with non-standard growth ⋮ \(\Gamma\)-convergence of the energy functionals for the variable exponent \(p(\cdot)\)-Laplacian and stability of the minimizers with respect to integrability

Cites Work

• On nonlinear Rayleigh quotients
• The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values
• Regularity results for a class of obstacle problems under nonstandard growth conditions
• Stability for the solutions of \(div(| \nabla u| ^{p-2}\nabla u)=f\) with varying p
• Two approximation problems in function spaces
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Stability of quasiminimizers of the p -Dirichlet integral with varying p on metric spaces
• Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent
• Pointwise Hardy inequalities
• A class of De Giorgi type and Hölder continuity
• Global integrability of the gradients of solutions to partial differential equations
• Gradient estimates for thep(x)-Laplacean system
• Regularity results for a class of functionals with non-standard growth

This page was built for publication: Global regularity and stability of solutions to elliptic equations with nonstandard growth