Mixed Boundary Value Problem on Hypersurfaces
Joint Authors
Tsutsunava, T.
DuDuchava, R.
Tsaava, M.
Source
International Journal of Differential Equations
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-17
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The purpose of the present paper is to investigate the mixed Dirichlet-Neumann boundary value problems for the anisotropic Laplace-Beltrami equation divC(A∇Cφ)=f on a smooth hypersurface C with the boundary Γ=∂C in Rn.
A(x) is an n×n bounded measurable positive definite matrix function.
The boundary is decomposed into two nonintersecting connected parts Γ=ΓD∪ΓN and on ΓD the Dirichlet boundary conditions are prescribed, while on ΓN the Neumann conditions.
The unique solvability of the mixed BVP is proved, based upon the Green formulae and Lax-Milgram Lemma.
Further, the existence of the fundamental solution to divS(A∇S) is proved, which is interpreted as the invertibility of this operator in the setting Hp,#s(S)→Hp,#s-2(S), where Hp,#s(S) is a subspace of the Bessel potential space and consists of functions with mean value zero.
American Psychological Association (APA)
DuDuchava, R.& Tsaava, M.& Tsutsunava, T.. 2014. Mixed Boundary Value Problem on Hypersurfaces. International Journal of Differential Equations،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-456892
Modern Language Association (MLA)
DuDuchava, R.…[et al.]. Mixed Boundary Value Problem on Hypersurfaces. International Journal of Differential Equations No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-456892
American Medical Association (AMA)
DuDuchava, R.& Tsaava, M.& Tsutsunava, T.. Mixed Boundary Value Problem on Hypersurfaces. International Journal of Differential Equations. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-456892
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-456892