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

Irina Kmit

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 4, page 507-517
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kmit, Irina. "$C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions." Commentationes Mathematicae Universitatis Carolinae 52.4 (2011): 507-517. <http://eudml.org/doc/246718>.

@article{Kmit2011,
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.},
author = {Kmit, Irina},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Nemytskii operators; Sobolev-type spaces of periodic functions; $C^1$-smoothness; Nemytskij operator; Sobolev space; travelling wave; smoothness},
language = {eng},
number = {4},
pages = {507-517},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions},
url = {http://eudml.org/doc/246718},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Kmit, Irina
TI - $C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 4
SP - 507
EP - 517
AB - 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.
LA - eng
KW - Nemytskii operators; Sobolev-type spaces of periodic functions; $C^1$-smoothness; Nemytskij operator; Sobolev space; travelling wave; smoothness
UR - http://eudml.org/doc/246718
ER -

References

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