Electron. J. Diff. Equ., Vol. 2012 (2012), No. 159, pp. 1-6.

Dirichlet-to-Neumann operator on the perturbed unit disk

Hassan Emamirad, Mohamed-Reza Mokhtarzadeh

Abstract:
This article concerns the Laplacian on a perturbed unit disk $\Omega_\epsilon=\{ z=r\exp(i\theta): r <1+\epsilon f(\theta) \}$, with dynamical boundary condition whose solution can be represented by a Dirichlet-to-Neumann semigroup. By neglecting the terms of order $\epsilon^2$, we obtain a simple expression which allows us to use the Chernoff's theorem for its approximation. As a motivation for this research, we present an example which shows the feasibility of applying of Chernoff's Theorem.

Submitted June 19, 2012. Published September 18, 2012.
Math Subject Classifications: 35J25, 47F05, 47D06.
Key Words: Dirichlet-to-Neumann operator, gamma-harmonic lifting.

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Hassan Emamirad
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
P.O. Box 19395-5746, Tehran, Iran
email: emamirad@ipm.ir
Mohamed-Reza Mokhtarzadeh
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
P.O. Box 19395-5746, Tehran, Iran
email: mrmokhtarzadeh@ipm.ir

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