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MiS Preprint
68/2003

On the regularity of critical points of polyconvex functionals

László Székelyhidi

Abstract

In this paper we are concerned with the question of regularity of

critical points for functionals of the type $$ I[u]=\int_{\Omega} F(Du) dx. $$ We construct a smooth, strongly polyconvex $F:\R^{2\times 2}\to\R$, and Lipschitzian weak solutions $u:\Omega\subset\R^2\to\R^2$ to the corresponding Euler-Lagrange system, which are nowhere $C^1$. Moreover we show that $F$ can be chosen in a way that these irregular weak solutions are weak local minimisers.

Received:
Jul 27, 2003
Published:
Jul 27, 2003
MSC Codes:
35B65, 35J60
Keywords:
regularity, elliptic systems, polyconvex

Related publications

inJournal
2004 Repository Open Access
László Székelyhidi

The regularity of critical points of polyconvex functionals

In: Archive for rational mechanics and analysis, 172 (2004) 1, pp. 133-152