Prof. Giovanni Pisante “A weighted anisotropic spectral optimization problem arising in population dynamic”

The plan of the talk is to discuss some recent results concerning a
weighted eigenvalue problem with anisotropic diffusion of p-Laplace
type in bounded Lipschitz domains under Robin boundary conditions.
The model aims to describe the dispersal of a population in a
heterogeneous environment Ω, triggered by a motion law so that each
individual moves with different probabilities depending on the direction
of the movement. In this context, the positive principal eigenvalue λ,
associated with the differential problem, turns out to be a threshold for
the survival of the population. Minimizing λ, with respect to the weight
or to other features of the model, endorses the chances of survival.

The presentation is based on a joint work with Benedetta Pellacci (University of
Campania ”L. Vanvitelli”) and Delia Schiera (Universidade de Lisboa).