Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 159, pp. 1-6.

Title: Dirichlet-to-Neumann operator on the perturbed unit disk

Authors: Hassan Emamirad (Inst. for Research in Fundamental Sciences, Iran)
         Mohamed-Reza Mokhtarzadeh (Inst. for Research in Fundamental Sciences, Iran)

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
 Chernoff's theorem for its approximation. As a motivation for
 this research, we present an example which shows the feasibility of 
 applying 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.