Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/194048
Title: | Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian |
Author: | Garofalo, Nicola Ros, Xavier |
Keywords: | Operadors diferencials parcials Teoria d'operadors Equacions en derivades parcials Processos estocàstics Partial differential operators Operator theory Partial differential equations Stochastic processes |
Issue Date: | 5-Jun-2019 |
Publisher: | European Mathematical Society Publishing House |
Abstract: | 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 $s \in(0,1)$. |
Note: | Versió postprint del document publicat a: https://doi.org/10.4171/RMI/1087 |
It is part of: | Revista Matematica Iberoamericana, 2019, vol. 35, num. 5, p. 1309-1365 |
URI: | http://hdl.handle.net/2445/194048 |
Related resource: | https://doi.org/10.4171/RMI/1087 |
ISSN: | 0213-2230 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
708573.pdf | 657.54 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.