Variational inequalities for the fractional Laplacian
type: Item
instance of: scholarly article
title: Variational inequalities for the fractional Laplacian
zbMATH Open document ID: 1368.35142
author: Roberta Musina
author: A. I. Nazarov
author: K. Sreenadh
published in: Potential Analysis
publication date: 2017-04-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1511.07417
review text: The interesting paper under review deals with the free boundary problem for the fractional Laplacian \[ \begin{cases} u\geq \psi & \text{in }\;\Omega,\\ (-\Delta)^su\geq f & \text{in}\;\Omega,\\ (-\Delta)^su= f & \text{in }\;\{u>\psi\},\\ u=0 & \text{in }\;\mathbb{R}^n\setminus\overline{\Omega}, \end{cases} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with \(n\geq 1,\) and \(s\in(0,1),\) the measurable function \(f\) and the distribution \(f\) are given. The authors show that, under quite mild assumptions on the data, the free boundary problem possesses a solution. The approach adopted relies on the study of broader class of problems regarding variational inequalities for the fractional Laplacian that admit solutions characterized as minimizers of suitable functionals.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J86
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35J88
zbMATH DE Number: 6708758
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: free boundary problems
zbMATH Keywords: variational inequalities
MaRDI profile type: Publication
OpenAlex ID: W2963223700
arXiv ID: 1511.07417
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DOI: 10.1007/S11118-016-9591-9
description: scientific article