Gradient estimates for \(p(x)\)-harmonic functions

DOI10.1007/S00229-009-0326-8zbMath1185.35077OpenAlexW2103769985MaRDI QIDQ2268171

Samia Challal, Abdeslem Lyaghfouri

Publication date: 10 March 2010

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-009-0326-8

zbMATH Keywords

\(p(x)\)-harmonic functions\(p(x)\)-Laplace equationa priori gradient estimate

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (7)

Hölder regularity of the gradient for the non-homogeneous parabolicp(x,t)-Laplacian equations ⋮ Hölder estimates for the elliptic p(x)-Laplacian equation with the logarithmic function ⋮ Hölder continuity for the solutions of the p(x)-Laplace equation with general right-hand side ⋮ Besov regularity estimates for the elliptic \(p(x)\)-Laplacian equation with the logarithmic growth ⋮ Hölder regularity for the general parabolic \(p(x, t)\)-Laplacian equations ⋮ Hölder continuity of \(p(x)\)-superharmonic functions ⋮ Weighted gradient estimates for the general elliptic \(p(x)\)-Laplacian equations

Cites Work

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• Global \(C^{1,\alpha}\) regularity for variable exponent elliptic equations in divergence form
• Hölder continuity of the gradient of p(x)-harmonic mappings
• Second order regularity for the p (x )-Laplace operator
• Gradient estimates for thep(x)-Laplacean system
• Regularity results for a class of functionals with non-standard growth
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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