A variational approach to parabolic systems

Paolo Marcellini

(UniversitĂ  di Firenze, Dipartimento di Matematica)

Event: ERC Workshop on Existence and Regularity for Nonlinear Systems of Partial Differential Equations

Date: Jul 02, 2014, time: 09:30

Abstract. We consider a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers. These evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals. In the simplest situation, with some growth conditions on f, the method provides the existence of global weak solutions to Cauchy-Dirichlet problems of parabolic systems. This is a joint collaboration with V. Bögelein and F. Duzaar.