4 papers
A discrete-time overdetermined problem for the heat equation
Lorenzo Cavallina, Andrea Pinamonti
In this paper, we consider a parabolic counterpart of Serrin's overdetermined problem, in which the overdetermined condition (constant flux condition) is imposed only on a discrete…
Elliptic and parabolic overdetermined problems in multi-phase settings
Lorenzo Cavallina, Giorgio Poggesi
The present paper provides symmetry results for a class of overdetermined problems of elliptic and parabolic type in multi-phase settings, including various extensions of remarkabl…
Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems
Lorenzo Cavallina, Giorgio Poggesi
We provide a full characterization of multi-phase problems under a large class of overdetermined Serrin-type conditions. Our analysis includes both symmetry and asymmetry (includin…
A miscellanea of qualitative and symmetry properties of the solutions to the two-phase Serrin's problem
Lorenzo Cavallina
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsio…