Dear all,

Here is the announcement of the next MAP seminar.

⟶ Thursday 12 December, at 11:30 in Aula Riunioni and online on Google Meet: https://meet.google.com/vtt-bhkm-tzc.

⟶ Speaker: Chiara Bernardini (Università di Trento)

⟶ Title: Serrin-type results for ring-shaped domains in Rⁿ

⟶ Abstract: We deal with the problem of characterizing rotationally symmetric solutions to

$\Delta u = n \text{ in } \Omega$

$u = 0 \text{ in } \partial\Omega$

when considering ring-shaped domains in the n-dimensional Euclidean space $\mathbb{R}^n$ (n ≥3). Taking advantage of a suitable conformal reformulation of the problem, we obtain some gradient estimates that will be fundamental to obtaining our main comparison result. In particular, if we assume that the set of maximum points of the solutions has positive ℋ ⁿ⁻¹-measure, we are able to characterize ring-shaped model solutions to the corresponding partially overdetermined problem. Our analysis also provides sufficient conditions for solutions to the problem to be rotationally symmetric.

This talk is based on a joint work with V.Agostiniani, S.Borghini and L.Mazzieri.

We remind you that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

See you soon,

The organizers:
Michele Caselli
Francesco Malizia

Jeremy Mirmina

Filippo Paiano

Leonardo Roveri