Harnack's inequality and the strong \(p(\cdot )\)-Laplacian

DOI10.1016/j.jde.2010.10.006zbMath1205.35084OpenAlexW2016278185MaRDI QIDQ618285

Tomasz Adamowicz, Peter A. Hästö

Publication date: 14 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.10.006

zbMATH Keywords

Harnack inequality\(p\)-Laplace equationDirichlet energysupersolutionvariable exponentCaccioppoli estimatenon-standard growth

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Perturbations in context of PDEs (35B20)

Related Items (19)

The boundary Harnack inequality for variable exponent \(p\)-Laplacian, Carleson estimates, barrier functions and \(p(\cdot)\)-harmonic measures ⋮ Hölder gradient regularity for the inhomogeneous normalized \(p(x)\)-Laplace equation ⋮ Higher integrability for nonlinear elliptic equations with variable growth ⋮ A minimization problem with variable growth on Nehari manifold ⋮ The sublinear problem for the 1-homogeneous 𝑝-Laplacian ⋮ Equivalence of viscosity and weak solutions for the normalized \(p(x)\)-Laplacian ⋮ The Liouville-type theorem for problems with nonstandard growth derived by Caccioppoli-type estimate ⋮ An eigenvalue problem with variable exponents ⋮ Kato’s inequality for the strong $p(\cdot )$-Laplacian ⋮ On the solvability of variable exponent differential inclusion systems with multivalued convection term ⋮ Phragmén-Lindelöf theorems for equations with nonstandard growth ⋮ Regularity of \(p(\cdot)\)-superharmonic functions, the Kellogg property and semiregular boundary points ⋮ Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients ⋮ Tug-of-war games with varying probabilities and the normalized \(p(x)\)-Laplacian ⋮ Gradient estimates for the strong \(p(x)\)-Laplace equation ⋮ Existence and multiplicity results for a new \(p(x)\)-Kirchhoff problem ⋮ Equivalence of weak and viscosity solutions to the \({\mathtt{p}}(x)\)-Laplacian in Carnot groups ⋮ Hölder regularity for the gradients of solutions of the strong \(p(x)\)-Laplacian ⋮ Existence of solutions for systems arising in electromagnetism

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