Bounded weak solutions to elliptic PDE with data in Orlicz spaces

David Cruz-Uribe, Scott Rodney

A classical regularity result is that non-negative solutions to the Dirichlet problem $\Delta u=f$ in a bounded domain $\Omega$, where $f\in L^q(\Omega )$, $q>\frac{n}{2}$, satisfy $\|u\|_{L^\infty(…