Estimativas de Carleman para uma classe de problemas parabólicos degenerados e aplicações à controlabilidade multiobjetivo.

Abstract

This work presents Carleman estimates to a class of degenerate parabolic problems over a square (in the two dimensional case) or a bounded interval (in the one dimensional case). We consider a di erential operator that degenerate only in a part of the boundary. Using semigroup theory, we prove well posedness results. Then, using suitables weight functions, we prove Carleman estimates and, as application, results on multi-objective controllability.