On the Treatment of a Dirichlet–Neumann Mixed Boundary Value Problem for Harmonic Functions by an Integral Equation Method
- 1 May 1977
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 8 (3) , 504-517
- https://doi.org/10.1137/0508038
Abstract
Using an approach which extends the well-known classical integral equation methods, we reduce a mixed boundary value problem for harmonic functions to a system consisting of two integral equations of the second kind. Existence is proved by the Fredholm alternative for compact operators. The integral equations can be solved apptgximately by successive iterations. Further investigations are made on the spectrum of the boundary integral operator.Keywords
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