Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany
Abstract:
Let be a bounded starshaped domain. In this note we consider critical points of the functional
where of class satisfies the natural growth
for some and , is suitably rank-one convex and in addition is strictly quasiconvex at . We establish uniqueness results under the extra assumption that is stationary at 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 Müller & Sverák (2003).