13 mar 2018 -- 14:30
Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma
In this talk, I will discuss Serrin's overdetermined boundary value problem -ΔSN u=1 in Ω u=0, ∂ηu=c on ∂Ω in subdomains Ω of the round unit sphere SN⊆RN+1, where ΔSN denotes the Laplace-Beltrami operator on SN. We call a subdomain Ω of SN a Serrin domain if it admits a solution of this overdetermined problem. In our main result, we construct Serrin domains in SN, N>2 which bifurcate from symmetric straight tubular neighborhoods of the equator. By this we complement recent rigidity results for Serrin domains on the sphere. This is joint work with M.M. Fall and I.A. Minlend (AIMS Senegal).