Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded \(\kappa\)-fat open sets
type: Item
instance of: scholarly article
title: Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded \(\kappa\)-fat open sets
zbMATH Open document ID: 1266.60137
author: Panki Kim
author: Hyunchul Park
author: Renming Song
published in: Potential Analysis
publication date: 2013-02-15T00:00:00Z
review text: The authors prove the following main result: Under suitable boundedness assumptions for the domain \(D\): if \(Y\) is a symmetric Lévy process with a Lévy density \(J^Y(x)= J(x)+ \sigma(x)\), with \(\sigma\) satisfying: \[ |\sigma|\leq c\max\{|x|^{-d+p},1\},\quad x\in R^d, \] then the \(D\)-domain Green function \(G^Y\) of \(Y^D\) is comparable to the \(D\)-domain Green function \(G^X_D\) of \(X^D\), that is: \[ c^{-1} G^Y_D(x,y)\leq G_D(x,y)\leq c,\;G_D(x,y),\quad x,y\in D, \] for a suitable constant \(c\).
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 6136698
zbMATH Keywords: Green functions
zbMATH Keywords: complete Green functions
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
full work available at URL: s11118-012-9278-9
OpenAlex ID: W1994988435
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DOI: 10.1007/S11118-012-9278-9
description: scientific article; zbMATH DE number 6136698