A note on higher regularity boundary Harnack inequality

DOI10.3934/dcds.2015.35.6155zbMath1336.35096arXiv1403.2588OpenAlexW2962967570MaRDI QIDQ255605

Daniela De Silva, Ovidiu V. Savin

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.2588

zbMATH Keywords

obstacle problem\(C^{k,\alpha}\) estimates

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)

Related Items (16)

Higher order parabolic boundary Harnack inequality in \(C^1\) and \(C^{k, \alpha}\) domains ⋮ Liouville type theorems and regularity of solutions to degenerate or singular problems. II: Odd solutions ⋮ Higher regularity of the free boundary in the obstacle problem for the fractional Laplacian ⋮ Regularity of free boundaries in obstacle problems ⋮ Regularity of the free boundary for the vectorial Bernoulli problem ⋮ Compactness methods for \(\gamma ^{1,\alpha }\) boundary Schauder estimates in Carnot groups ⋮ A parabolic analogue of the higher-order comparison theorem of De Silva and Savin ⋮ Boundary pointwise regularity and applications to the regularity of free boundaries ⋮ \(C^{2, \alpha}\) regularity of free boundaries in parabolic non-local obstacle problems ⋮ Linear stability implies nonlinear stability for Faber-Krahn-type inequalities ⋮ Higher regularity of the free boundary in the obstacle problem for the fractional heat operator ⋮ Higher regularity of the free boundary in the parabolic Signorini problem ⋮ Regularity of the optimal sets for some spectral functionals ⋮ Obstacle problems for integro-differential operators: higher regularity of free boundaries ⋮ The fractional obstacle problem with drift: higher regularity of free boundaries ⋮ A new boundary Harnack principle (equations with right hand side)

Cites Work

• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Hölder domains and the boundary Harnack principle
• Regularity in elliptic free boundary problems. I
• The obstacle problem revisited
• On boundary behavior of harmonic functions in Hölder domains
• On the Boundary Values of Harmonic Functions
• Unnamed Item

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