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$C^{1}$ -smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

Irina Kmit (2011)

Commentationes Mathematicae Universitatis Carolinae

We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the $C^{1}$ -continuity property of these operators over Sobolev-type spaces of periodic functions.

Calcul fonctionnel dans certains espaces de Besov

G. Bourdaud, D. Kateb (1990)

Annales de l'institut Fourier

On montre que les fonctions qui opèrent, par composition a gauche, sur l’espace de Besov d’exposant $s$ , avec $0 < s < 1 / q$ , dans l’espace euclidien de dimension $n$ , sont précisément les fonctions lipschitziennes.

Displaying 1 – 9 of 9

$C^{1}$ -smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

Calcul fonctionnel dans certains espaces de Besov

C.L. Siegel's Linearization Theorem in Infinite Dimensions.

Compactness and weak compactness of gradient maps

Concerning interior mapping theorem

Constant and variable drop theorems on metrizable locally convex spaces

Continuity and differentiability properties of nonlinear operators

Continuity of Nemyckij's operator in Hölder spaces

Continuous extensions of multifunctions

Currently displaying 1 – 9 of 9