We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality ...

We study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$. Dirichlet conditions are imposed along $\partial\Omega$ ...