Optimization of the principal eigenvalue of the pseudo p-Laplacian operator with robin boundary conditions

This paper is concerned with an optimization problem related to the pseudo p-Laplacian eigenproblem, with Robin boundary conditions. The principal eigenvalue is minimized over a rearrangement class generated by a fixed positive function. Existence and optimality condition are proved. The popular case where the generator is a characteristic function is also considered. In this case the method of domain derivative is used to capture qualitative features of the optimal solutions.