Partial regularity of strong local minimizers in the multi-dimensional calculus of variations

Jan Kristensen and Ali Taheri

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Submission date: 29. Aug. 2001
Pages: 27
published in: Archive for rational mechanics and analysis, 170 (2003) 1, p. 63-89 
DOI number (of the published article): 10.1007/s00205-003-0275-4
Bibtex

Abstract:
Let be a bounded domain and a given strongly quasiconvex integrand of class satisfying the growth condition

for some c>0 and . Consider the multiple integral

where . The main result of the paper is that any strong local minimizer of is of class for any on an open set of full n-dimensional measure. In the case of weak local minimizers we establish the same result under the extra assumption that the oscillations in the gradient of the minimizer are not too large. Without such an assumption weak local minimizers need not be partially regular. This is shown by a class of examples that are obtained by suitably modifying the arguments of S. Müller and V. Sverak.