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Continuity and differentiability of multivalued superposition operators with atoms and parameters II
- 1.0374006 - MÚ 2013 RIV DE eng J - Journal Article
Väth, Martin
Continuity and differentiability of multivalued superposition operators with atoms and parameters II.
Zeitschrift für Analysis und Ihre Anwendungen. Roč. 31, č. 2 (2012), s. 139-160. ISSN 0232-2064. E-ISSN 1661-4534
R&D Projects: GA AV ČR IAA100190805
Institutional research plan: CEZ:AV0Z10190503
Keywords : superposition operator * Nemytskij operator * multivalued map
Subject RIV: BA - General Mathematics
Impact factor: 0.620, year: 2012
http://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=31&iss=2&rank=2
For a given single- or multivalued function f and "atoms'' S i , let S f (λ,x) be the set of all measurable selections of the function sf(λ,s,x(s)) which are constant on each Si. It is discussed how this definition must be extended so that Sf 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.
Permanent Link: http://hdl.handle.net/11104/0207031
Number of the records: 1