An extended variational theory for nonlinear evolution equations via modular spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F21%3A43902765" target="_blank" >RIV/60076658:12510/21:43902765 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/21:50018547

Výsledek na webu

<a href="https://epubs.siam.org/doi/10.1137/20M1385251" target="_blank" >https://epubs.siam.org/doi/10.1137/20M1385251</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/20M1385251" target="_blank" >10.1137/20M1385251</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An extended variational theory for nonlinear evolution equations via modular spaces

Popis výsledku v původním jazyce

We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly nonreflexive and nonseparable spaces. The pivoting point is to establish a novel variational structure, based on abstract modular spaces associated to a given convex function. First, we show that the new variational triple is suited for framing the evolution, in the sense that a novel duality pairing can be introduced and a generalized computational chain rule holds. Second, we prove well-posedness in an extended variational sense for evolution equations, without relying on any reflexivity assumption and any polynomial requirement on the nonlinearity. Finally, we discuss several important applications that can be addressed in this framework: these cover, but are not limited to, equations in Musielak-Orlicz-Sobolev spaces, such as variable exponent, Orlicz, weighted Lebesgue, and double-phase spaces.

Název v anglickém jazyce

An extended variational theory for nonlinear evolution equations via modular spaces

Popis výsledku anglicky

We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly nonreflexive and nonseparable spaces. The pivoting point is to establish a novel variational structure, based on abstract modular spaces associated to a given convex function. First, we show that the new variational triple is suited for framing the evolution, in the sense that a novel duality pairing can be introduced and a generalized computational chain rule holds. Second, we prove well-posedness in an extended variational sense for evolution equations, without relying on any reflexivity assumption and any polynomial requirement on the nonlinearity. Finally, we discuss several important applications that can be addressed in this framework: these cover, but are not limited to, equations in Musielak-Orlicz-Sobolev spaces, such as variable exponent, Orlicz, weighted Lebesgue, and double-phase spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-19018Y" target="_blank" >GJ20-19018Y: Jemné analytické a topologické metody pro variační problémy a modelování</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

—

Svazek periodika

53

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

4865-4907

Kód UT WoS článku

000692288300038

EID výsledku v databázi Scopus

2-s2.0-85114743215