Weighted Multipolar Hardy Inequalities in R^N and Kolmogorov Type Operators

The main purpose of the thesis, which describes the topics I was involved and the results achieved so far, is to introduce the multipolar weighted Hardy inequalities in R^N in the context of the study of Kolmogorov type operators perturbed by singular potentials and of the related evolution problems. The thesis describes, in the first part (Chapter 1), the reference results we can find in literature about the behaviour of the operators with inverse square potentials in the unipolar and multipolar case (existence and nonexistence of positive solutions to evolution problems with Schrodinger and Kolmogorov type operators and positivity of the quadratic form associated with Schrodinger operators). Furthermore we recall the Hardy inequalities in the case of Lebesgue measure and in the weighted case. In the second part (Chapters 2 and 3) we report our results about Kolmogorov type operators and weighted Hardy inequalities.