The boundedness and Hölder continuity of weak solutions to elliptic equations involving variable exponents and critical growth

DOI10.1016/j.jde.2022.01.004zbMath1483.35054arXiv2010.15098OpenAlexW4221081073MaRDI QIDQ2074436

Yun-Ho Kim, Chao Zhang, Patrick Winkert, Ky Ho

Publication date: 10 February 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.15098

zbMATH Keywords

a priori bounds\(p(\cdot)\)-LaplacianDe Giorgi iterationvariable exponent Lebesgue and Sobolev spaceslocalization method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Quasilinear elliptic equations (35J62) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (12)

A new class of double phase variable exponent problems: existence and uniqueness ⋮ Notes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent ⋮ Existence and multiplicity of solutions to concave-convex-type double-phase problems with variable exponent ⋮ A multiplicity theorem for anisotropic Robin equations ⋮ Existence, uniqueness and asymptotic behavior of parametric anisotropic \((p, q)\)-equations with convection ⋮ Hölder continuity for the solutions of the p(x)-Laplace equation with general right-hand side ⋮ On sufficient ``local conditions for existence results to generalized \(p(.)\)-Laplace equations involving critical growth ⋮ New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems ⋮ A second-order Sobolev regularity for \(p(x)\)-Laplace equations ⋮ On the L^∞‐regularity for fractional Orlicz problems via Moser's iteration ⋮ Nehari manifold approach for superlinear double phase problems with variable exponents ⋮ \((p, q)\)-equations with negative concave terms

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