An Epiperimetric Inequality for the Regularity of Some Free Boundary Problems: The 2‐Dimensional Case

DOI10.1002/cpa.21785zbMath1429.35214arXiv1612.01623OpenAlexW2613152039MaRDI QIDQ3120799

Bozhidar Velichkov, Luca Spolaor

Publication date: 19 March 2019

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.01623

zbMATH Keywords

variational inequalitiesfree boundary problemsregularity of solutioncusps of a free boundary

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Free boundary problems for PDEs (35R35) Blow-up in context of PDEs (35B44)

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On the logarithmic epiperimetric inequality for the obstacle problem ⋮ Regularity of the free boundary for the vectorial Bernoulli problem ⋮ Epsilon-regularity for the solutions of a free boundary system ⋮ The symmetric (log-)epiperimetric inequality and a decay-growth estimate ⋮ Regularity of the optimal sets for the second Dirichlet eigenvalue ⋮ On the asymptotic behavior of the solutions to parabolic variational inequalities ⋮ A two-phase problem with Robin conditions on the free boundary ⋮ Free boundary regularity for a multiphase shape optimization problem ⋮ Regularity of the free boundary for the two-phase Bernoulli problem ⋮ A logarithmic epiperimetric inequality for the obstacle problem ⋮ Uniqueness of the blowup at isolated singularities for the Alt-Caffarelli functional ⋮ Existence and regularity of optimal shapes for elliptic operators with drift ⋮ Branch points for (almost-)minimizers of two-phase free boundary problems

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