Marcinkiewicz estimates for solutions of some elliptic problems with nonregular data

The method introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity (L(p), Marcinkiewicz or C(0,alpha)) of the weak solutions u is an element of W(0)(1,2) (Omega) of Dirichlet problems hinges on the handle of inequalities concerning the integral of |del u vertical bar(2) on the subsets where vertical bar u( x)vertical bar is greater than k. In this framework, here we give a contribution with the study of the Marcinkiewicz regularity of the gradient of infinite energy solutions of Dirichlet problems with nonregular data.