The obstacle problem for a higher order fractional Laplacian

DOI10.1007/s00526-023-02557-9zbMath1529.35107arXiv2305.07201OpenAlexW4386095255MaRDI QIDQ6137580

Arshak Petrosyan, Alaa Haj Ali, Donatella Danielli

Publication date: 4 September 2023

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.07201

zbMATH Keywords

thin obstacle problemweighted b-biharmonic operator

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Free boundary problems for PDEs (35R35) Variational methods for higher-order elliptic equations (35J35) Fractional partial differential equations (35R11) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)

Cites Work

• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Optimal regularity of lower dimensional obstacle problems
• The \(s\)-polyharmonic extension problem and higher-order fractional Laplacians
• Regularity of the obstacle problem for a fractional power of the laplace operator
• The structure of the free boundary for lower dimensional obstacle problems
• Further regularity for the signorini problem
• An Extension Problem Related to the Fractional Laplacian
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