Invariance of the Fredholm radius of the Neumann operator. (English) Zbl 0707.35049

Medková, Dagmar

Čas. Pěstování Mat. 115, No. 2, 147-164 (1990).

In an earlier paper, M. Dont and E. Dontová [ibid. 112, 269-283 (1987; Zbl 0657.31004)] proved that the Fredholm radius of the Neumann operator is invariant with respect to conformal deformations of the Jordan domain. The present author shows that, in \({\mathbb{R}}^ m\) for any \(m\geq 2\), the Fredholm radius of the Neumann operator is unchanged if the domain is deformed by a diffeomorphism which preserves angles on a specific portion of the boundary.

Reviewer: N.A.Watson

MSC:

35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P05	General topics in linear spectral theory for PDEs
31B20	Boundary value and inverse problems for harmonic functions in higher dimensions
47A53	(Semi-) Fredholm operators; index theories
47F05	General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)

Keywords:

Neumann operator; invariant; conformal deformations; Fredholm radius