17 mar 2010

**Abstract.**

The first Calculus of Variations seminar of the second semester will be:

Wednesday, March 17 5 pm, Dipartimento di Matematica, Sala Seminari.

Prof. Thomas Schmidt (FAU Erlangen-Nuernberg)

Title: Quasiconvex integrals with $(p,q)$-growth

Abstract: We investigate the minimization problem for multi-dimensional variational integrals, defined on vector-valued functions, with respect to a Dirichlet boundary condition. If the integrand grows like a fixed power then existence and partial regularity of minimizers are well-understood and related to the notion of quasiconvexity. Here, we are interested in the case where the integrand can be estimated from above and below in terms of two different powers, a model case being polyconvex integrands with lower exponent possibly smaller than the space dimension. We will discuss two approaches to existence and partial regularity in this setting, one of them based on the notion of $W^{1,p}$-quasiconvexity, the other (and more interesting) one relying on subtle properties of a relaxation procedure.