||Dynamical approach to an overdetermined problem in potential theory
Dynamical approach to an overdetermined problem in potential theory
小野寺, 有紹Onodera, Michiaki
796 , 2016-03 , Elsevier
We introduce a new approach for studying the uniqueness and stability of a domain admitting the solvability of an overdetermined problem. One of the key observations is that the deformation of a continuously varying domain for a parametrized overdetermined problem forms an analytic semiflow. This allows us to obtain the uniqueness of a domain for the original ``stationary'' overdetermined problem together with a quantitative estimate of its shape by clarifying the dynamical structure of the semiflow.