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Elliptic Interface Problems in Axisymmetric Domains. Part I: Singular Functions of Non ‐ Tensorial Type
Author(s) -
Heinrich Bernd,
Nicaise Serge,
Weber Beate
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211860109
Subject(s) - mathematics , sobolev space , mathematical analysis , sequence (biology) , poisson's equation , fourier transform , smoothness , elliptic curve , finite element method , fourier series , interface (matter) , gibbs isotherm , chemistry , organic chemistry , adsorption , genetics , physics , biology , thermodynamics
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 2D‐variational 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 II 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.