On the regularity of critical points of polyconvex functionals

László Székelyhidi

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Submission date: 27. Jul. 2003
Pages: 23
published in: Archive for rational mechanics and analysis, 172 (2004) 1, p. 133-152 
DOI number (of the published article): 10.1007/s00205-003-0300-7
Bibtex
with the following different title: The regularity of critical points of polyconvex functionals
MSC-Numbers: 35B65, 35J60
Keywords and phrases: regularity, elliptic systems, polyconvex
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Abstract:
In this paper we are concerned with the question of regularity of critical points for functionals of the type

We construct a smooth, strongly polyconvex , and Lipschitzian weak solutions to the corresponding Euler-Lagrange system, which are nowhere . Moreover we show that F can be chosen in a way that these irregular weak solutions are weak local minimisers.