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Polyconvexity for functions of a system of closed differential forms

  1. 1.
    0485750 - MÚ 2019 RIV DE eng J - Článek v odborném periodiku
    Šilhavý, Miroslav
    Polyconvexity for functions of a system of closed differential forms.
    Calculus of Variations and Partial Differential Equations. Roč. 57, č. 1 (2018), č. článku 26. ISSN 0944-2669. E-ISSN 1432-0835
    Institucionální podpora: RVO:67985840
    Klíčová slova: polyconvexity
    Obor OECD: Applied mathematics
    Impakt faktor: 1.652, rok: 2018
    https://link.springer.com/article/10.1007%2Fs00526-017-1298-2

    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.
    Trvalý link: http://hdl.handle.net/11104/0280693

     
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