Lucio Cadeddu

A short note on the mean exit time of the Brownian motion

We investigate the functional Ω↦ℰ(Ω) where Ω runs through the set of compact domains of fixed volume v in any Riemannian manifold (M,g) and where ℰ(Ω) is the mean exit time from Ω of the Brownian motion. We give an alternative analytical proof of a well-known fact on its critical points proved by McDonald: the critical points of ℰ(Ω) are harmonic domains.

Spaces of anisotropic ultradifferentiable functions and local solvability for semilinear partial differential equations

We propose constructions of multiparameter depending scales of Banach spaces of anisotropic ultra-differentiable functions and investigate their invariance under changes of the variables. We prove new local solvability results in such spaces for some classes of linear and semilinear partial differential equations with multiple characteristics.