Boundedness of the extremal solution of some p-Laplacian problems

In this article we consider the p-Laplace equation on a smooth bounded domain of with zero Dirichlet boundary conditions. Under adequate assumptions on f we prove that the extremal solution of this problem is in the energy class independently of the domain. We also obtain Lq and W1,q estimates for such a solution. Moreover, we prove its boundedness for some range of dimensions depending on the nonlinearity f.http://www.sciencedirect.com/science/article/B6V0Y-4KFV38H-1/1/cea49519619442ca6f3831d7928ae4e