Uniform estimates for fundamental solutions associated with nonlocal Dirichlet forms
type: Item
instance of: scholarly article
title: Uniform estimates for fundamental solutions associated with nonlocal Dirichlet forms
zbMATH Open document ID: 0867.35123
author: Takashi Komatsu
published in: Osaka Journal of Mathematics
publication date: 1996-07-14T00:00:00Z
review text: The paper studies fundamental solutions of parabolic equations associated with pseudodifferential operators with non-continuous coefficients. The solutions can be obtained as transition functions of a Feller process associated with a Dirichlet form of non-local type. More precisely, the processes under consideration are stable type processes associated with measures of the form \[ K(t,dx,dy)=k(t,x,y)|x-y|^{-d-\alpha}dx dy, \] where \(k\) is a measurable function that is continuous with respect to the time variable and that satisfies \[ c_1\leq k(t,x,y)\leq c_2+c_3t^{-\gamma/\alpha}|x-y|^\gamma. \] The author proves a lower estimate and the Hölder continuity for the fundamental solution of the corresponding equation. The proof is based on moment bounds.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 902835
zbMATH Keywords: fundamental solutions
zbMATH Keywords: non-continuous coefficients
zbMATH Keywords: Dirichlet form of non-local type
zbMATH Keywords: lower estimate
zbMATH Keywords: Hölder continuity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 902835