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MiS Preprint

On the regularity of critical points of polyconvex functionals

László Székelyhidi


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.

MSC Codes:
35B65, 35J60
regularity, elliptic systems, polyconvex

Related publications

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