Gradient potential estimates in non-linear elliptic obstacle problems with measure data

DOI10.1016/j.jfa.2012.01.003zbMath1238.35030OpenAlexW2016937184MaRDI QIDQ765908

Christoph Scheven

Publication date: 22 March 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2012.01.003

zbMATH Keywords

\(p\)-Laplacianregularity of solutionsmeasure data problemselliptic obstacle problemsnon-linear potential theory

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) PDEs with measure (35R06)

Related Items (16)

A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem ⋮ Regularity estimates for singular parabolic measure data problems with sharp growth ⋮ Potential estimates for elliptic measure data problems with irregular obstacles ⋮ Fractional differentiability for elliptic double obstacle problems with measure data ⋮ Calderón–Zygmund type estimates for singular quasilinear elliptic obstacle problems with measure data ⋮ Unnamed Item ⋮ Nonlinear measure data problems ⋮ Elliptic obstacle problems with measure data: potentials and low order regularity ⋮ Gradient potential estimates for elliptic obstacle problems ⋮ Nonlinear gradient estimates for elliptic double obstacle problems with measure data ⋮ Gradient estimates for nonlinear elliptic double obstacle problems ⋮ Weighted distribution approach to gradient estimates for quasilinear elliptic double-obstacle problems in Orlicz spaces ⋮ Unnamed Item ⋮ Global weighted estimates for nonlinear elliptic obstacle problems over Reifenberg domains ⋮ Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains ⋮ Gradient potential estimates in elliptic obstacle problems with Orlicz growth

Cites Work

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• Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles
• Gradient estimates via linear and nonlinear potentials
• Gradient continuity estimates
• Local Lipschitz regularity for degenerate elliptic systems
• Gradient potential estimates
• Nonlinear elliptic and parabolic equations involving measure data
• Pathological solutions to elliptic problems in divergence form with continuous coefficients
• A note on Riesz potentials
• The Wiener test and potential estimates for quasilinear elliptic equations
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Existence and uniqueness of solutions for nonlinear obstacle problems with measure data
• Maximizing the \(L^ \infty{}\) norm of the gradient of solutions to the Poisson equation
• Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
• Elliptic obstacle problems with measure data: potentials and low order regularity
• Gradient estimates via non-linear potentials
• Weakly Differentiable Functions
• Nonlinear Elliptic Equations with Right Hand Side Measures
• Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations
• On the weak continuity of elliptic operators and applications to potential theory
• Unilateral problems with measure data.

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