Illinois Journal of Mathematics

Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains

Steve Hofmann, John Lewis, and Marius Mitrea

Full-text: Open access

Abstract

We study the invertibility of $\lambda I+K$ in $L^p(\partial\Omega\times\mathbf{R})$, for $p$ near $2$ and $\lambda\in\mathbf{R}$, $|\lambda|\geq\sfrac12$, where $K$ is the caloric double layer potential operator and $\Omega$ is a Lipschitz domain. Applications to transmission boundary value problems are also presented.

Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1345-1361.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138108

Digital Object Identifier
doi:10.1215/ijm/1258138108

Mathematical Reviews number (MathSciNet)
MR2037007

Zentralblatt MATH identifier
1036.35067

Subjects
Primary: 35K10: Second-order parabolic equations
Secondary: 35P05: General topics in linear spectral theory 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 45B05: Fredholm integral equations

Citation

Hofmann, Steve; Lewis, John; Mitrea, Marius. Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains. Illinois J. Math. 47 (2003), no. 4, 1345--1361. doi:10.1215/ijm/1258138108. https://projecteuclid.org/euclid.ijm/1258138108


Export citation