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Title: Convolution type operators with symmetry in Bessel potential spaces
Author: Castro, Luís Pinheiro de
Speck, Frank-Olme
Keywords: Convolution type operator
Boundary value problem
Explicit solution
Sobolev space
Issue Date: 25-Feb-2017
Publisher: Springer International Publishing
Abstract: Convolution type operators with symmetry appear naturally in boundary value problems for elliptic PDEs in symmetric or symmetrizable domains. They are defined as truncations of translation invariant operators in a scale of Sobolev-like spaces that are convolutionally similar to subspaces of even or odd functionals. The present class, as a basic example, is closely related to the Helmholtz equation in a quadrant, where a possible solution is "symmetrically" extended to a half-plane. Explicit factorization methods allow the representation of resolvent operators in closed analytic form for a large class of boundary conditions including the two-impedance and the oblique derivative problems. Moreover they allow fine results on the regularity and asymptotic behavior of the solutions.
ISBN: 978-3-319-47077-1
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FAAG - Capítulo de livro

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