Second order regularity for the p (x )-Laplace operator

DOI10.1002/mana.200810285zbMath1226.35025OpenAlexW2038995907MaRDI QIDQ5199438

Samia Challal, Abdeslem Lyaghfouri

Publication date: 16 August 2011

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200810285

zbMATH Keywords

regularityvariable exponent Sobolev spaces\(p(x)\)-Laplace operator

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60)

Related Items (14)

An inhomogeneous singular perturbation problem for the \(p(x)\)-Laplacian ⋮ Global weighted estimates in Orlicz spaces for second-order nondivergence parabolic equations ⋮ A remark on the two-phase obstacle-type problem for the \(p\)-Laplacian ⋮ Hölder regularity of the gradient for the non-homogeneous parabolicp(x,t)-Laplacian equations ⋮ Interior regularity to the steady incompressible shear thinning fluids with non-standard growth ⋮ A second-order Sobolev regularity for \(p(x)\)-Laplace equations ⋮ Second order regularity for the \(p (x)\)-Laplace equations with \(L^2\) data on the right-hand side ⋮ Higher regularity of solutions of singular parabolic equations with variable nonlinearity ⋮ Regularity of flat free boundaries for a \(p(x)\)-Laplacian problem with right hand side ⋮ \(H^2\) regularity for the \(p(x)\)-Laplacian in two-dimensional convex domains ⋮ Gradient estimates for \(p(x)\)-harmonic functions ⋮ Hölder regularity for the general parabolic \(p(x, t)\)-Laplacian equations ⋮ A minimization problem for the \(p(x)\)-Laplacian involving area ⋮ Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity

Cites Work

• Unnamed Item
• Global \(C^{1,\alpha}\) regularity for variable exponent elliptic equations in divergence form
• Regularity for a more general class of quasilinear equations
• On some variational problems
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• Hölder continuity of the gradient of p(x)-harmonic mappings
• Regularity results for a class of functionals with non-standard growth
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

This page was built for publication: Second order regularity for the p (x )-Laplace operator