Quasiconvexity and uniqueness of stationary points in the multi-dimensional calculus of variation

Taheri, Ali (2003) Quasiconvexity and uniqueness of stationary points in the multi-dimensional calculus of variation. Proceedings of the American Mathematical Society, 131 (10). 3101 - 3107. ISSN 0002-9939

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Abstract

Let Omega subset of R-n be a bounded starshaped domain. In this note we consider critical points (u) over bar is an element of (ξ) over bary + W-0(1,p) (Omega; R-m) of the functional F(u, Omega) := integral(Omega) f(delu(y))dy, where f : R-m x n --> R of class C-1 satisfies the natural growth \f (xi)\ less than or equal to c(1+ \xi\(p)) for some 1less than or equal top<∞ and c>0, is suitably rank-one convex and in addition is strictly quasiconvex at (ξ) over bar is an element of R-m x n. We establish uniqueness results under the extra assumption that F is stationary at (u) over bar with respect to variations of the domain. These statements should be compared to the uniqueness result of Knops & Stuart (1984) in the smooth case and recent counterexamples to regularity produced by Muller Sverak (2003).

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Ali Taheri
Date Deposited: 06 Feb 2012 21:26
Last Modified: 10 Jul 2012 14:46
URI: http://sro.sussex.ac.uk/id/eprint/31257
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