Marcinkiewicz estimates for solutions of some elliptic problems with nonregular data

Abstract

The method introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity (Lp, Marcinkiewicz or C0,α) of the weak solutions u ∈ W1,20(Ω) of Dirichlet problems hinges on the handle of inequalities concerning the integral of |∇u|2 on the subsets where |u(x)| 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. © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2008.