Journal Article Dynamical approach to an overdetermined problem in potential theory

小野寺, 有紹  ,  Onodera, Michiaki

106 ( No. 4 )  , pp.768 - 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.

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