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.