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) 
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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.