JournalszaaVol. 31, No. 2pp. 139–160

Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters II

  • Martin Väth

    Czech Academy of Sciences, Prague, Czech Republic
Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters II cover
Download PDF

Abstract

For a given single- or multivalued function ff and “atoms” SiS_i, let Sf(λ,x)S_f(\lambda,x) be the set of all measurable selections of the function s \mapsto f(\lambda, s, x(s)) which are constant on each SiS_i. It is discussed how this definition must be extended so that SfS_f can serve as a right-hand side for PDEs when one is looking for weak solutions in Sobolev spaces. Continuity and differentiability of the corresponding operators are studied.

Cite this article

Martin Väth, Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters II. Z. Anal. Anwend. 31 (2012), no. 2, pp. 139–160

DOI 10.4171/ZAA/1452