Almost everywhere regularity for the free boundary of the 𝑝-harmonic obstacle problem 𝑝>2

DOI10.1090/SPMJ/1654zbMath1465.35084arXiv1611.04397OpenAlexW3160363533MaRDI QIDQ4989681

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Publication date: 26 May 2021

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04397

zbMATH Keywords

Hausdorff measureCarleson measure\(p\)-Laplace operator

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Free boundary problems for PDEs (35R35) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (2)

Analysis of blow-ups for the double obstacle problem in dimension two ⋮ Regularity of the free boundary in the biharmonic obstacle problem

Cites Work

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• Remarks on Hausdorff measure and stability for the \(p\)-obstacle problem \((1 < p < 2)\)
• On the \(A\)-obstacle problem and the Hausdorff measure of its free boundary
• The obstacle problem revisited
• Hausdorff measure and stability for the \(p\)-obstacle problem \((2<p<\infty)\).
• On the porosity of free boundaries in degenerate variational inequalities
• On the singular sets of minimizers of the Mumford-Shah functional
• Rectifiable sets, densities and tangent measures
• The zero level set for a certain weak solution, with applications to the Bellman equations
• On the Obstacle Problem for Quasilinear Elliptic Equations of p Laplacian Type

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