Equazioni alle derivate parziali ellittiche con crescita quadratica rispetto al gradiente

This thesis deal with a class of nonlinear partial differential equations of elliptic type with Dirichlet boundary conditions in bounded domains. More specifically, we treat a class of equations with lower order terms that have the so-called natural growth with respect to gradient. We analyzed the cases in which the right hand side of the equation is singular (either a $L^1$ function or a measure) and in which the lower order term is singular as the solution approaches zero (i.e. the boundary value). Both existence and nonexistence results are considered.