Invariance of the Fredholm radius of an operator in potential theory. (English) Zbl 0657.31004

Dont, Miroslav; Dontová, Eva

Čas. Pěstování Mat. 112, 269-283 (1987).

One of the classical methods of solving the Dirichlet problem in \(R^ n\) is the method of integral equations. Using this method for a non-smooth regions it is useful to know the Fredholm radius of an integral operator playing a role in the method. It is shown in the paper that in the case of a Jordan domain in the plane the Fredholm radius of that operator does not change under the conformal mapping of the boundary.

MSC:

31A25	Boundary value and inverse problems for harmonic functions in two dimensions
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

Dirichlet problem; method of integral equations; non-smooth regions; Fredholm radius; Jordan domain in the plane; conformal mapping