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Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian


Garofalo, Nicola; Ros-Oton, Xavier (2019). Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian. Revista matemática iberoamericana, 35(5):1309-1365.

Abstract

We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, min{(−Δ)su,u−φ}=0 in Rn, for general obstacles φ. 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∈(0,1).

Abstract

We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, min{(−Δ)su,u−φ}=0 in Rn, for general obstacles φ. 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∈(0,1).

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:4 June 2019
Deposited On:09 Jan 2020 12:37
Last Modified:29 Jul 2020 12:59
Publisher:Universidad de La Rioja ; Dialnet
ISSN:0213-2230
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4171/rmi/1087

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