Polyconvexity for functions of a system of closed differential forms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00485750" target="_blank" >RIV/67985840:_____/18:00485750 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00526-017-1298-2" target="_blank" >http://dx.doi.org/10.1007/s00526-017-1298-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00526-017-1298-2" target="_blank" >10.1007/s00526-017-1298-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polyconvexity for functions of a system of closed differential forms

Popis výsledku v původním jazyce

This paper deals with the weakened convexity properties, mult. ext. quasiconvexity, mult. ext. one convexity, and mult. ext. polyconvexity, for integral functionals of the form I(omega1,...,omegas)=...(omega1,...,omegas)dx where omega1, ... , omegas are closed differential forms on a bounded open set Omega ... Rn. The main results of the paper are explicit descriptions of mult. ext. quasiaffine and mult ext. polyconvex functions. It turns out that these two classes consist, respectively, of linear and convex combinations of the set of all wedge products of exterior powers of the forms omega1,..., omegas. Thus, for example, a function f= f(omega1,..., omegas) is mult. ext. polyconvex if and only if (Formula presented.) where q1, ..., qs ranges a finite set of integers and phi is a convex function. An existence theorem for the minimum energy state is proved for mult. ext. polyconvex integrals.

Název v anglickém jazyce

Polyconvexity for functions of a system of closed differential forms

Popis výsledku anglicky

This paper deals with the weakened convexity properties, mult. ext. quasiconvexity, mult. ext. one convexity, and mult. ext. polyconvexity, for integral functionals of the form I(omega1,...,omegas)=...(omega1,...,omegas)dx where omega1, ... , omegas are closed differential forms on a bounded open set Omega ... Rn. The main results of the paper are explicit descriptions of mult. ext. quasiaffine and mult ext. polyconvex functions. It turns out that these two classes consist, respectively, of linear and convex combinations of the set of all wedge products of exterior powers of the forms omega1,..., omegas. Thus, for example, a function f= f(omega1,..., omegas) is mult. ext. polyconvex if and only if (Formula presented.) where q1, ..., qs ranges a finite set of integers and phi is a convex function. An existence theorem for the minimum energy state is proved for mult. ext. polyconvex integrals.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

e-ISSN

—

Svazek periodika

57

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

26

Strana od-do

—

Kód UT WoS článku

000424746800027

EID výsledku v databázi Scopus

2-s2.0-85040328363