Weak compactness of Fréchet-derivatives: application to composition operators
Copyright policy )Weak compactness of Fréchet-derivatives: application to composition operators
AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.
Representation and superposition of functions, weakly compact map, Banach spaces, Fréchet derivatives, Calculus of functions taking values in infinite-dimensional spaces, compactness properties, Linear operators on function spaces (general), Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, calculus of variations, superposition operators
Representation and superposition of functions, weakly compact map, Banach spaces, Fréchet derivatives, Calculus of functions taking values in infinite-dimensional spaces, compactness properties, Linear operators on function spaces (general), Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, calculus of variations, superposition operators
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