Qualitative properties of singular solutions to nonlocal problems
type: Item
instance of: scholarly article
title: Qualitative properties of singular solutions to nonlocal problems
zbMATH Open document ID: 1391.35384
author: Luigi Montoro
author: Fabio Punzo
author: Berardino Sciunzi
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2018-06-27T00:00:00Z
review text: By using the moving plane method and under suitable assumptions on the semilinear term, the authors prove symmetry and monotonicity properties for the positive weak solutions to the Dirichlet problem for the fractional Laplacian \[ \begin{cases} (-\Delta)^su=f(x,u) & \text{ in }\Omega\setminus\Gamma,\\ u>0 & \text{ in }\Omega\setminus\Gamma,\\ u=0 & \text{ in }\mathbb R^N\setminus\Omega \end{cases} \] in the case when \(\alpha\in(0,1)\), \(N>2s\), \(\Omega\) is either a bounded domain with smooth boundary or the whole space \(\mathbb R^N\) and the compact singular set \(\Gamma\subset\Omega\) has zero \(s\)-capacity.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35B51
zbMATH DE Number: 6894904
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: qualitative properties
zbMATH Keywords: moving plane method
MaRDI profile type: Publication
full work available at URL: s10231-017-0710-z
OpenAlex ID: W2766826216
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DOI: 10.1007/S10231-017-0710-Z
description: scientific article; zbMATH DE number 6894904