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

Steve Hofmann, John L. Lewis, Marius Mitrea

Type: Article

Publication Date: 2003-10-01

Citations: 9

DOI: https://doi.org/10.1215/ijm/1258138108

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.

Locations

Illinois Journal of Mathematics - View - PDF

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Works Cited by This (26)

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+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+	Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials	1997	Steve Hofmann
+	Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems	1994	Carlos E. Kenig
+	Partial Differential Equations of Parabolic Type	1964	Avner Friedman
+	Les Méthodes directes en théorie des équations elliptiques	1967	Jindřich Nečas Jean Dhombres Marie-Ève Maillé Philippe Robba
+	The Spectral Radius of the Classical Layer Potentials on Convex Domains	1992	Eugene B. Fabes Mark E. Sand Jin Keun Seo
+ PDF Chat	Stability results on interpolation scales of quasi-Banach spaces and applications	1998	N. J. Kalton Marius Mitrea
+	THE INITIAL DIRICHLET BOUNDARY VALUE PROBLEM FOR GENERAL SECOND ORDER PARABOLIC SYSTEMS IN NONSMOOTH MANIFOLDS	2001	Marius Mitrea
+	Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains	1984	Gregory C. Verchota
+	L'integrale de Cauchy Definit un Operateur Borne sur L 2 Pour Les Courbes Lipschitziennes	1982	Ronald R. Coifman Alan McIntosh Yves Meyer