D. G. Afonso

Non-radial minimizers for the first eigenvalue of the Laplacian in cones and a related overdetermined problem

In this work, we consider relative overdetermined problems for the first eigenfunction of the Laplacian for domains in cones, and the related question of minimizing the first eigenvalue among sets of a given fixed measure. By means of a shape derivative analysis, we show that the spherical sector is a critical shape an...