Remarks on local boundedness and local holder continuity of local weak solutions to anisotropic \(p\)-Laplacian type equations

DOI10.1007/BF03377399zbMath1386.35113arXiv1610.09509OpenAlexW2544313168MaRDI QIDQ1691839

Vincenzo Vespri, Ugo Gianazza, Emmanuele DiBenedetto

Publication date: 25 January 2018

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.09509

zbMATH Keywords

ellipticHölder continuityanisotropic \(p\)-Laplacian

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (24)

Local Lipschitz continuity for energy integrals with slow growth ⋮ Regularity of weak supersolutions to elliptic and parabolic equations: lower semicontinuity and pointwise behavior ⋮ An introduction to Barenblatt solutions for anisotropic \(p\)-Laplace equations ⋮ Unnamed Item ⋮ Regularity under general and \(p,q\)-growth conditions ⋮ On the local behavior of local weak solutions to some singular anisotropic elliptic equations ⋮ Unnamed Item ⋮ Existence of infinitely many solutions for an anisotropic equation using genus theory ⋮ Nonstandard competing anisotropic \((p,q)\)-Laplacians with convolution ⋮ Higher integrability for anisotropic parabolic systems of \(p\)-Laplace type ⋮ A positive solution for an anisotropic \((p,q)\)-Laplacian ⋮ Local boundedness of weak solutions to elliptic equations with \(p, q\)-growth ⋮ Regularity for local minima of a special class of vectorial problems with fully anisotropic growth ⋮ Unnamed Item ⋮ Existence of positive eigenfunctions to an anisotropic elliptic operator via the sub-supersolution method ⋮ Hölder regularity for bounded solutions to a class of anisotropic operators ⋮ Lipschitz regularity for orthotropic functionals with nonstandard growth conditions ⋮ Local boundedness of quasi-minimizers of fully anisotropic scalar variational problems ⋮ Local regularity for an anisotropic elliptic equation ⋮ Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations ⋮ On Hölder continuity and equivalent formulation of intrinsic Harnack estimates for an anisotropic parabolic degenerate prototype equation ⋮ Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence ⋮ Higher integrability and stability of \((p,q)\)-quasiminimizers ⋮ Local continuity of singular anisotropic parabolic equations with variable growth

Cites Work

• Unnamed Item
• Unnamed Item
• Regularity of minimizers under limit growth conditions
• Degenerate parabolic equations
• Local boundedness of minimizers in a limit case
• Hölder continuity of solutions to an anisotropic elliptic equation
• Growth conditions and regularity. A counterexample
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Teoremi di inclusione per spazi di Sobolev non isotropi
• The boundedness of generalized solutions of elliptic differential equations
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• On the theory of embedding of anisotropic Sobolev spaces

This page was built for publication: Remarks on local boundedness and local holder continuity of local weak solutions to anisotropic \(p\)-Laplacian type equations