Advanced Studies in Pure Mathematics

A variational problem involving a polyconvex integrand

Wilfrid Gangbo

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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.

Article information

Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 115-130

Received: 31 October 2012
Revised: 13 March 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document euclid.aspm/1539916035

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws
Secondary: 49J40: Variational methods including variational inequalities [See also 47J20]

Polyconvexity duality nonlinear elasticity theory Ogden material


Gangbo, Wilfrid. A variational problem involving a polyconvex integrand. Variational Methods for Evolving Objects, 115--130, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710115.

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