A-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00470210" target="_blank" >RIV/67985556:_____/17:00470210 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21110/17:00315656

Výsledek na webu

<a href="http://dx.doi.org/10.1515/acv-2015-0009" target="_blank" >http://dx.doi.org/10.1515/acv-2015-0009</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/acv-2015-0009" target="_blank" >10.1515/acv-2015-0009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals

Popis výsledku v původním jazyce

We state necessary and sufficient conditions for weak lower semicontinuity of integral functionals of the form u bar right arrow integral(Omega) h(x, u(x)) dx, where h is continuous and possesses a positively p-homogeneous recession function, p > 1, and u is an element of L-p(Omega, R-m) lives in the kernel of a constant-rank first-order differential operator A which admits an extension property. In the special case A = curl, apart from the quasiconvexity of the integrand, the recession function's quasiconvexity at the boundary in the sense of Ball and Marsden is known to play a crucial role. Our newly defined notions of A-quasiconvexity at the boundary, generalize this result. Moreover, we give an equivalent condition for the weak lower semicontinuity of the above functional along sequences weakly converging in L-p(Omega, R-m) and approaching the kernel of A even if A does not have the extension property.

Název v anglickém jazyce

A-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals

Popis výsledku anglicky

We state necessary and sufficient conditions for weak lower semicontinuity of integral functionals of the form u bar right arrow integral(Omega) h(x, u(x)) dx, where h is continuous and possesses a positively p-homogeneous recession function, p > 1, and u is an element of L-p(Omega, R-m) lives in the kernel of a constant-rank first-order differential operator A which admits an extension property. In the special case A = curl, apart from the quasiconvexity of the integrand, the recession function's quasiconvexity at the boundary in the sense of Ball and Marsden is known to play a crucial role. Our newly defined notions of A-quasiconvexity at the boundary, generalize this result. Moreover, we give an equivalent condition for the weak lower semicontinuity of the above functional along sequences weakly converging in L-p(Omega, R-m) and approaching the kernel of A even if A does not have the extension property.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Advances in Calculus of Variations

ISSN

1864-8258

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

19

Strana od-do

49-67

Kód UT WoS článku

000391557700003

EID výsledku v databázi Scopus

2-s2.0-85013656827