Global differentiability results for weak solutions of nonlinear elliptic problems with controlled growths

The author considers the problem of global differentiability of solutions for a quasilinear, second order, Dirichlet problem relative to a bounded open subset $\Omega\subset{\Bbb R}^n$, $n>2$. Solutions here considered are Sobolev ones of the type $u\in H^1(\Omega,{\Bbb R}^N)$, and with the term global differentiable solutions are meant solutions of the type $u\in H^2(\Omega,{\Bbb R}^N)$. \par The main result is an existence theorem of solutions of such a type, under suitable conditions, and also a global second order estimate. The methodology adopted is in the framework of functional analysis, following some previous results by S. Campanato (see the quoted papers in references).