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VOL. 67 | 2015 A variational problem involving a polyconvex integrand
Wilfrid Gangbo

Editor(s) Luigi Ambrosio, Yoshikazu Giga, Piotr Rybka, Yoshihiro Tonegawa

Abstract

Existence of solutions to systems of parabolic equations obtained from polyconvex functions, remains a challenge in PDEs. In the current notes, we keep our focus on a variational problem which originates from a discretization of such a system. We state a duality result for a functional whose integrand is polyconvex and fails to satisfy growth conditions imposed in the standard theory of the calculus of variations.

The current notes are based on a work with Roméo Awi [3] and on a lecture we gave at the meeting “Variatonal Methods for Evolving Objects”, July 30–August 03, 2012, Sapporo, Japan. We express our gratitude to the organizers of the meeting for their support and generous invitation.

Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1364.49014
MathSciNet: MR3587449

Digital Object Identifier: 10.2969/aspm/06710115

Subjects:
Primary: 35L65
Secondary: 49J40

Rights: Copyright © 2015 Mathematical Society of Japan

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