Asymptotics of the Spectral Function for the Steklov Problem in a Family of Sets with Fractal Boundaries∗
نویسندگان
چکیده
In this paper we find the asymptotic behavior of the spectral counting function for the Steklov problem in a family of self similar domains with fractal boundaries. Using renewal theory, we show that the main term in the asymptotics depends on the Minkowski dimension of the boundary. Also, we compute explicitly a three term expansion for a family of self similar sets, and a two term asymptotic expansion for a family of non self similar sets.
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