Preprint 29/2001
Quasiconvexity and uniqueness of stationary points in the multi-dimensional calculus of variations
Ali Taheri
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Submission date: 02. Nov. 2001
Pages: 8
published in: Proceedings of the American Mathematical Society, 131 (2003) 10, p. 3101-3107 (electronic) 
DOI number (of the published article): 10.1090/S0002-9939-03-06852-7
Bibtex
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Abstract:
Let 
be a starshaped domain. In this note we consider critical points 
of the functional 
where 
of class 
, is suitably rank-one convex, and in addition strictly quasiconvex at 
. We establish uniqueness results under the extra assumption that 
is stationary at 
with respect to variations of the domain. These results should be compared to the ones by Knops and Stuart and recent counterexamples produced by Müller and Sverak.