2026-04-17T02:45:11Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1940482025-12-05T09:59:04Zcom_2072_1057col_2072_478917col_2072_478920

Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian Garofalo, Nicola Ros, Xavier Operadors diferencials parcials Teoria d'operadors Equacions en derivades parcials Processos estocàstics Partial differential operators Operator theory Partial differential equations Stochastic processes We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, $\min \left\{(-\Delta)^s u, u-\varphi\right\}=0$ in $\mathbb{R}^n$, for general obstacles $\varphi$. Our main result establishes the complete structure and regularity of the singular set. To prove it, we construct new monotonicity formulas of Monneau-type that extend those in those of Garofalo-Petrosyan to all $s \in(0,1)$. 2023-02-23T14:02:24Z 2023-02-23T14:02:24Z 2019-06-05 2023-02-23T14:02:24Z info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Versió postprint del document publicat a: https://doi.org/10.4171/RMI/1087 Revista Matematica Iberoamericana, 2019, vol. 35, num. 5, p. 1309-1365 https://doi.org/10.4171/RMI/1087 (c) European Mathematical Society Publishing House, 2019 info:eu-repo/semantics/openAccess European Mathematical Society Publishing House Articles publicats en revistes (Matemàtiques i Informàtica)