Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional Laplacian

DOI10.1016/j.na.2021.112473zbMath1471.35297arXiv2006.12928OpenAlexW3177393974MaRDI QIDQ2048341

Simon Eberle, Xavier Ros-Oton, Georg Sebastian Weiss

Publication date: 5 August 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.12928

zbMATH Keywords

full classification of global solutionsthin obstacle problem)

Mathematics Subject Classification ID

Free boundary problems for PDEs (35R35) Fractional partial differential equations (35R11) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)

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Cites Work

• Null quadrature domains
• On quadrature domains and the Schwarz potential
• The obstacle problem revisited
• Newtonian potential theory for unbounded sources and applications to free boundary problems
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• The local regularity of solutions of degenerate elliptic equations
• Attraction des ellipsoïdes homogènes et réciproques d'un théorème de Newton
• Characterizing compact coincidence sets in the obstacle problem—a short proof
• An Extension Problem Related to the Fractional Laplacian
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