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Laplace–Beltrami equation on hypersurfaces and Γ-convergence
A. Razmadze Mathematical Institute, Tbilisi State University.
A. Razmadze Mathematical Institute, Tbilisi State University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2017 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476Article in journal (Refereed) Epub ahead of print
Abstract [en]

A mixed boundary value problem for the stationary heat transfer equation in a thin layer around a surface C with the boundary is investigated. The main objective is to trace what happens in Γ-limit when the thickness of the layer converges to zero. The limit Dirichlet BVP for the Laplace–Beltrami equation on the surface is described explicitly, and we show how the Neumann boundary conditions in the initial BVP transform in the Γ-limit. For this, we apply the variational formulation and the calculus of Günter's tangential differential operators on a hypersurface and layers, which allow global representation of basic differential operators and of corresponding boundary value problems in terms of the standard Euclidean coordinates of the ambient space Rn.

Place, publisher, year, edition, pages
2017.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-62549DOI: 10.1002/mma.4331OAI: oai:DiVA.org:ltu-62549DiVA: diva2:1082660
Available from: 2017-03-17 Created: 2017-03-17 Last updated: 2017-03-17

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