Premium
Kernel Properties and Representations of Boundary Integral Operators
Author(s) -
Schwab C.,
Wendland W. L.
Publication year - 1992
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.19921560113
Subject(s) - mathematics , mixed boundary condition , mathematical analysis , boundary (topology) , boundary value problem , elliptic operator , singular boundary method , kernel (algebra) , pure mathematics , boundary element method , finite element method , physics , thermodynamics
Boundary integral operators arise in the reduction to the boundary method for solving elliptic boundary value problems. These are classical pseudodifferential operators of integer order on the boundary. In order to exploit these boundary integral operators for computational methods one needs explicit knowledge of the corresponding kernel properties in the framework of Hadamard finite part regularization, explicit representation based on local polar coordinates and explicit transformation under the change of the parametric representation of the boundary manifold. Here we present these properties for the special case of a (piecewise) smooth two‐dimensional boundary surface immersed into ℝ 3 .