Heat kernel bounds and desingularizing weights.
type: Item
instance of: scholarly article
title: Heat kernel bounds and desingularizing weights.
zbMATH Open document ID: 1036.35044
DOI: 10.1016/S0022-1236(03)00018-1
author: D. Massart
published in: Journal of Functional Analysis
publication date: 2003-09-04T00:00:00Z
review text: The authors study the parabolic operator \(\partial_t -\Delta_x +V(t,x)\) in \(\mathbb{R}^1_+\times \mathbb{R}^d\), \(d\geq 1\), with a potential \(V=V^+-V^-\), \(V^\pm \geq 0\) assumed to be from a parabolic Kato class. Let \(Z_V(t,x;s,y)\) be the kernel corresponding to this operator and \(\Gamma (t,x)\) be the heat kernel. The authors prove that there are constants \(c_i^\pm >0\) and \(\omega_i\) such that \[ c_1^- \exp(\omega_1(t-s))) \Gamma (c_2^-(t-s),x-y)\leq Z_V(t,x;y,s)\leq c_1^+ \exp(\omega_2 (t-s)) \Gamma(c_2^+(t-s),x-y). \]
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K10
zbMATH DE Number: 1974788
zbMATH Keywords: parabolic Kato class
reviewed by: Dagmar Medková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974788