Minimal thickness and uniqueness of kernel functions for the heat equation in several variables
type: Item
instance of: scholarly article
title: Minimal thickness and uniqueness of kernel functions for the heat equation in several variables
zbMATH Open document ID: 0824.35042
author: Masaharu Nishio
author: Noriaki Suzuki
published in: Osaka Journal of Mathematics
publication date: 1995-02-09T00:00:00Z
review text: A kernel function for the heat equation on a domain \(\Omega\) in \(\mathbb{R}^{n + 1}\) is a nonnegative temperature which vanishes continuously on the parabolic boundary of \(\Omega\), except at a given point which may be at infinity, but does not vanish identically. Uniqueness of such functions (up to a multiplicative constant) is established for certain domains of the form \(\Omega = \{(x,t) : T > t > \varphi (x)\}\), and their images under Appell transformation, where \(T\) is a positive constant and \(\varphi\) a nonnegative, upper semicontinuous function.
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 31C35
zbMATH DE Number: 720167
zbMATH Keywords: Lipschitz domain
zbMATH Keywords: kernel function
reviewed by: Neil A. Watson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 720167