Ana Margarida Ribeiro, Department of Mathematical Sciences, Carnegie Mellon University
Vectorial differential inclusions, generalized notions of convexity and applications to non quasiconvex minimizing problems
We will consider problems on differential inclusions in a vectorial framework. The study of sufficient conditions for this kind of problems has been developed by Dacorogna-Marcellini and Muller-Sverak and has lead to the introduction of notions of convex hulls for sets in a generalized sense which are not always coherent with the classical convex theory.
In a first part of the talk we will introduce a notion of quasiconvex set which will be supported by its relations with the other convexity notions, namely polyconvexity and rank-1 convexity. We will then consider a differential inclusion problem involving the determinant function and the singular values. This problem can be solved by means of the Baire categories method and it will be used to illustrate how differential inclusions can be useful to solve non quasiconvex minimizing problems.
The results presented were obtained in collaboration with B. Dacorogna.
TUESDAY, October 30, 2007