Elliptic Interface Problems in Axisymmetric Domains. Part I: Singular Functions of Non - Tensorial Type
✍ Scribed by Bernd Heinrich; Serge Nicaise; Beate Weber
- Book ID
- 102942459
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 758 KB
- Volume
- 186
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
We study the regularity of solutions of interface problems for the Poisson equation in axisynunetric domains. The Fourier decomposition of the 3D-problem into a sequence of 2Dvariational equations end uniform (with respect to the sequence parameter) a prior; estimates of their solutions are derived. Some non-tensorial singular functions describing the behaviour of the solution near interface edges are given and the smoothness of the stress intensity distribution as well as the tangential regularity are characterized in tenns of Sobolev spaces. In a forthcoming part I1 of this paper, the results will be applied to error estimates of the so-called Fourier-finite-element method for solving approximately elliptic interface problems in 3D. Technische Universiiii Chemniiz -Zwickau Fakuliii fir Mathematik Cambrtsis D -091 07 Chemniiz Germany e -mail: heinrich4maihcmaiik.iuchcmniiz.de Univcraiit dc Valenciennes ei du Hainaui LIMAV and URA D 751 CNRS "GAT" Inaiiiui d e s Sciences ei Techniques d e Valcncicnnea