Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains
type: Item
instance of: scholarly article
title: Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains
zbMATH Open document ID: 1036.35067
author: Marius Mitrea
author: Steve Hofmann
author: John L. Lewis
published in: Illinois Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
review text: Let \(\Omega \) be a bounded Lipschitz domain and \(T>0\). Let \(K\) be the caloric double layer potential operator on \(\partial \Omega \times (0,T)\). The authors show that there is \(\varepsilon >0\) such that \(\lambda I+K\) is invertible on \(L^p(\partial \Omega \times (0,T))\) for each \(p\in (2- \varepsilon,2+\varepsilon )\) and a real \(\lambda \) with \(| \lambda | \geq 1/2\). A similar result for harmonic double layer potentials was shown by \textit{L. Escauriaza, E. Fabes} and \textit{G. Verchota} [Proc. Am. Math. Soc. 115, 1069--1076 (1992; Zbl 0761.35013)]. This result was used for the study of the initial transmission boundary value problem for the heat equation.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 31B10
zbMATH DE Number: 2028876
zbMATH Keywords: heat equation
zbMATH Keywords: transmission problem
zbMATH Keywords: double layer potential
zbMATH Keywords: single layer potential
reviewed by: Dagmar Medková
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028876