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

zbMATH Open1247.47044arXiv1107.4484MaRDI QIDQ2897370

Irina Kmit

Publication date: 10 July 2012

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1107.4484

zbMATH Keywords

Sobolev spacesmoothnessNemytskij operatortravelling wave

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30)

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