Dirichlet-to-Neumann operator on the perturbed unit disk

This article concerns the Laplacian on a perturbed unit disk $Omega_epsilon={ z=rexp(iheta): r <1+epsilon f(heta) }$, 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 e...

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Bibliographic Details
Main Authors:	Hassan Emamirad, Mohamed-Reza Mokhtarzadeh
Format:	Article
Language:	English
Published:	Texas State University 2012-09-01
Series:	Electronic Journal of Differential Equations
Subjects:	Dirichlet-to-Neumann operator, gamma-harmonic lifting
Online Access:	http://ejde.math.txstate.edu/Volumes/2012/159/abstr.html

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spelling	doaj-cb6b704b4b5f42ed96b18bb094891c072020-11-24T21:07:54ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-09-012012159,16Dirichlet-to-Neumann operator on the perturbed unit diskHassan EmamiradMohamed-Reza MokhtarzadehThis article concerns the Laplacian on a perturbed unit disk $Omega_epsilon={ z=rexp(iheta): r <1+epsilon f(heta) }$, 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. http://ejde.math.txstate.edu/Volumes/2012/159/abstr.htmlDirichlet-to-Neumann operator, gamma-harmonic lifting
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hassan Emamirad Mohamed-Reza Mokhtarzadeh
spellingShingle	Hassan Emamirad Mohamed-Reza Mokhtarzadeh Dirichlet-to-Neumann operator on the perturbed unit disk Electronic Journal of Differential Equations Dirichlet-to-Neumann operator, gamma-harmonic lifting
author_facet	Hassan Emamirad Mohamed-Reza Mokhtarzadeh
author_sort	Hassan Emamirad
title	Dirichlet-to-Neumann operator on the perturbed unit disk
title_short	Dirichlet-to-Neumann operator on the perturbed unit disk
title_full	Dirichlet-to-Neumann operator on the perturbed unit disk
title_fullStr	Dirichlet-to-Neumann operator on the perturbed unit disk
title_full_unstemmed	Dirichlet-to-Neumann operator on the perturbed unit disk
title_sort	dirichlet-to-neumann operator on the perturbed unit disk
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2012-09-01
description	This article concerns the Laplacian on a perturbed unit disk $Omega_epsilon={ z=rexp(iheta): r <1+epsilon f(heta) }$, 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.
topic	Dirichlet-to-Neumann operator, gamma-harmonic lifting
url	http://ejde.math.txstate.edu/Volumes/2012/159/abstr.html
work_keys_str_mv	AT hassanemamirad dirichlettoneumannoperatorontheperturbedunitdisk AT mohamedrezamokhtarzadeh dirichlettoneumannoperatorontheperturbedunitdisk
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Dirichlet-to-Neumann operator on the perturbed unit disk

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