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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.