Interior regularity for solutions to obstacle problems

DOI10.1016/0362-546X(86)90113-6zbMath0603.49006OpenAlexW1970968605MaRDI QIDQ3739762

William P. Ziemer, J. H. Michael

Publication date: 1986

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(86)90113-6

zbMATH Keywords

regularityweak solutionsWiener conditionquasilinear variational inequalities

Mathematics Subject Classification ID

Related Items (39)

The Wiener test and potential estimates for quasilinear elliptic equations ⋮ Existence of solutions to obstacle problems ⋮ Regularity of Supersolutions ⋮ The Wiener criterion and quasilinear uniformly elliptic equations ⋮ A-superharmonic functions and supersolutions of degenerate elliptic equations ⋮ Regularity of weak supersolutions to elliptic and parabolic equations: lower semicontinuity and pointwise behavior ⋮ Global regularity and stability of solutions to obstacle problems with nonstandard growth ⋮ Hölder continuity of the gradient for degenerate variational inequalities ⋮ Regularity results for solutions to a class of obstacle problems ⋮ Lipschitz continuity results for a class of obstacle problems ⋮ Representation, relaxation and convexity for variational problems in Wiener spaces ⋮ An epiperimetric inequality for the lower dimensional obstacle problem ⋮ Higher differentiability for bounded solutions to a class of obstacle problems with \((p, q)\)-growth ⋮ Lipschitz regularity for constrained local minimizers of convex variational integrals with a wide range of anisotropy ⋮ Removable sets for Hölder continuous solutions of quasilinear elliptic equations with lower order terms ⋮ Hölder continuity of solutions for quasilinear elliptic equations with gradient terms and measures ⋮ Level-set inequalities on fractional maximal distribution functions and applications to regularity theory ⋮ Higher regularity of the solution to the \(p\)-Laplacian obstacle problem ⋮ Boundedness and differentiability for nonlinear elliptic systems ⋮ The classical obstacle problem for nonlinear variational energies ⋮ Gradient continuity for nonlinear obstacle problems ⋮ The Hölder continuity for the gradient of solutions to one-sided obstacle problems ⋮ Regularity for certain degenerate elliptic double obstacle problems ⋮ \(A_{p}\)-weight and integrability of solutions in obstacle problems ⋮ Boundary regularity of weak solutions to nonlinear elliptic obstacle problems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Local Behavior of Solutions of Quasilinear Elliptic Equations With General Structure ⋮ A Wiener-type condition for boundary continuity of quasi-minima of variational integrals ⋮ Regularity of Weak Solutions of Parabolic Variational Inequalities ⋮ Higher differentiability for solutions to a class of obstacle problems ⋮ On the Wiener Criterion and Quasilinear Obstacle Problems ⋮ Regularity results for a class of obstacle problems with nonstandard growth ⋮ Regularity results for a class of non-differentiable obstacle problems ⋮ Regularity results for quasilinear degenerate elliptic obstacle problems in Carnot groups ⋮ An oscillation estimate to a variational inequality ⋮ A priori gradient bounds and local \(C^{1,\alpha}\)-estimates for (double) obstacle problems under non-standard growth conditions ⋮ A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems ⋮ Pointwise regularity of solutions to nonlinear double obstacle problems

Cites Work

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• Über das Verhalten der Lösung des Dirichletproblems für eine elliptische Gleichung zweiter Ordnung in divergenter Form in der Nähe des Randes
• Linear and quasilinear elliptic equations
• Sulla hölderianità delle soluzioni di alcune disequazioni variazionali con condizioni unilatere al bordo
• On functions of bounded mean oscillation
• Mean Values of Subsolutions of Elliptic and Parabolic Equations
• On harnack type inequalities and their application to quasilinear elliptic equations

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