Open Access
2013 On Ventcel's Type Boundary Condition for Laplace Operator in a Sector
Petar Popivanov, Angela Slavova
J. Geom. Symmetry Phys. 31: 119-130 (2013). DOI: 10.7546/jgsp-31-2013-119-130


This paper deals with classical solutions of the Dirichlet-Ventcel boundary value problem (BVP) for the Laplace operator in bounded sector in the plane having opening of the corresponding angle $ \varphi_{0} > 0 $. Ventcel BVP is given by second order differential operator on the boundary satisfying Lopatinksii condition there. As the boundary is non smooth, two different cases appear: $ \frac{\pi}{\varphi_{0}} $ is irrational and $ \frac{\pi}{\varphi_{0}} $ is an integer. At first we prove uniqueness result via the maximum principle and then existence of the classical solution. To do this we apply two different approaches: the machinery of the small denominators and the concept of Green function.


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Petar Popivanov. Angela Slavova. "On Ventcel's Type Boundary Condition for Laplace Operator in a Sector." J. Geom. Symmetry Phys. 31 119 - 130, 2013.


Published: 2013
First available in Project Euclid: 26 May 2017

zbMATH: 1291.35048
MathSciNet: MR3154687
Digital Object Identifier: 10.7546/jgsp-31-2013-119-130

Rights: Copyright © 2013 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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