Regularity results for some elliptic and parabolic problems

The present thesis deals with the regularity of solutions to nonlinear partial differential equations of elliptic and parabolic type, and it collects some results obtained during the last three years under the supervision of Prof. Ugo Gianazza The first part concernes the study of singular porous medium type equations: we start proving H\"older regularity for solutions of variable sign, then we continue with an Harnack type inequality for positive solutions. The second part treats existence and regularity results for a class of non-coercive elliptic equations with discontinuous coefficients, extending a paper by Prof. Lucio Boccardo.