Advanced Studies in Pure Mathematics

A variational problem involving a polyconvex integrand

Wilfrid Gangbo

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1539916035

Digital Object Identifier
doi:10.2969/aspm/06710115

Mathematical Reviews number (MathSciNet)
MR3587449

Zentralblatt MATH identifier
1364.49014

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

Keywords
Polyconvexity duality nonlinear elasticity theory Ogden material

Citation

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. https://projecteuclid.org/euclid.aspm/1539916035


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