Continuity and differentiability of multivalued superposition operators with atoms and parameters II

0374006 - MÚ 2013 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA AV ČR IAA100190805
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: superposition operator * Nemytskij operator * multivalued map
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.620, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0207031