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

Source: [$C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions](<https://www.sota2.com/research/paper/68fa4f801e209131ce963ad5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:19:45.016Z

Authors: Irina Kmit

Published: 2011-07-22T11:31:30.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1107.4484>)

[PDF](<https://arxiv.org/pdf/1107.4484.pdf>)