Nonlinear elastic membranes involving the p-Laplacian operator

This paper concerns an optimization problem related to the Poisson equation for the p-Laplace operator, subject to homogeneous Dirichlet boundary conditions. Physically the Poisson equation models, for example, the deformation of a nonlinear elastic membrane which is fixed along the boundary, under load. A particular situation where the load is represented by a characteristic function is investigated.