Universidad de Granada

Abstract: A shape monotonicity problem asks which shape yields a better value for a given functional. As a model case, we consider eccentric annuli of fixed radii and study the monotonicity of the first Dirichlet eigenvalue with respect to the distance between the centers. We further investigate shape monotonicity problems for eccentric annuli with mixed boundary conditions. To study these problems, we analyze the associated heat kernels and develop probabilistic methods.