The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel Method
- 1 July 1992
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 45 (1) , 135-177
- https://doi.org/10.1080/00036819208840093
Abstract
We consider the double layer potential operator W defined on the polyhedral boundary of an infinite cone and prove the invertibility of (I±2W) in the space of continuous functions. To do this we define an operator-valued symbol function for W and show that the spectral radii of its values are less than one half. In the last part of this paper we consider a piecewise constant collocation method for the numerical solution of the double layer potential equation over the boundary of a bounded polyhedron.Keywords
This publication has 6 references indexed in Scilit:
- Eigenvalues for spherical domains with corners via boundary integral equationsIntegral Equations and Operator Theory, 1991
- Corner singularity for transmission problems in three dimensionsIntegral Equations and Operator Theory, 1989
- Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domainsJournal of Functional Analysis, 1984
- The Dirichlet Problem in Non-Smooth DomainsAnnals of Mathematics, 1981
- The Neumann problem on Lipschitz domainsBulletin of the American Mathematical Society, 1981
- Integral Operators in Potential TheoryLecture Notes in Mathematics, 1980