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
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Let tex2html_wrap_inline19 be a starshaped domain. In this note we consider critical points tex2html_wrap_inline21 of the functional
where tex2html_wrap_inline25 of class tex2html_wrap_inline27, is suitably rank-one convex, and in addition strictly quasiconvex at tex2html_wrap_inline29. We establish uniqueness results under the extra assumption that tex2html_wrap_inline31 is stationary at tex2html_wrap_inline33 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.

24.11.2021, 02:11