Note on contractivity of the Neumann operator. (English) Zbl 0657.31010

Medková, Dagmar

Čas. Pěstování Mat. 112, 197-208 (1987).

The paper deals with the Neumann operator on the space of signed measures on boundary, for which the measure of the whole space equals zero. An example of a set, the complement of which is a non-convex bounded set, and at the same time the corresponding Neumann operator is contractiv on this space, is shown.

MSC:

31B20

Boundary value and inverse problems for harmonic functions in higher dimensions

Keywords:

generalized normal derivative; perimeter; hit; Neumann operator; space of signed measures; non-convex; contractiv