Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 115 - 130
A variational problem involving a polyconvex integrand
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  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.
Received: 31 October 2012
Revised: 13 March 2013
First available in Project Euclid: 19 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L65: Conservation laws
Secondary: 49J40: Variational methods including variational inequalities [See also 47J20]
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