| In this thesis we study some particular features of parabolic differential operators given by Lu=divAX ,t1u -6t u, where A(X, t) = ( ai,j(x, t)) is an n x n symmetric matrix of bounded measurable functions defined on Rn+1 satisfying a certain ellipticity condition. To be more precise, we solve two questions in two different chapters. In Chapter 3 we give a sufficient condition for the mutual absolute continuity of the parabolic measure associated to L, and the surface measure of a non-cylindrical domain O. This will allow us, in Chapter 4, to solve a Dirichlet problem associated to Lu = 0 in this time-varying domain, and with boundary data in the Lebesgue space Lp(∂O). |
