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On the regularity of critical points of polyconvex functionals
László SzékelyhidiAbstract
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:
- 27.07.03
- Published:
- 27.07.03
- MSC Codes:
- 35B65, 35J60
- Keywords:
- regularity, elliptic systems, polyconvex