Global Lipschitz regularity for a class of quasilinear elliptic equations

The Lipschitz continuity of solutions to Dirichlet and Neumann problems for nonlinear elliptic equations, including the p-Laplace equation, is established under minimal integrability assumptions on the data and on the curvature of the boundary of the domain. The case of arbitrary bounded convex domains is also included. The results have new consequences even for the Laplacian. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.