Analytic and geometric properties of functions with dislocations singularity (13h30)

Riccardo Scala (Weierstrass Institute (WIAS), Berlin)

Abstract: We study the nature of the singularities of the strain fields due to the presence of dislocations in a crystal. We prove and collect some measure theoretic properties of such singularities. Among them, we give the explicit description of the boundary of the graph defined by deformation fields, which, in the presence of dislocations, are well-defined as torus-valued maps. Using such description we are able to deal and solve some variational problems involving such maps, as, for instance, problems of minimization of energies depending on the elastic strain and the dislocation density as well.

Lp -Continuity of Solutions to Parabolic Free Boundary Problems (14h15)

E. Zaouche (Ecole Normale Supérieure, Algerie)

Abstract: We consider a class of parabolic free boundary problems. We establish some properties of the solutions, including L -regularity in time and a monotonicity property, from which we deduce strong Lp-continuity in time.
Key-words: Free boundary problem, parabolic equation, monotonicity, regularity.

These seminars are supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.