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Lp-theory of boundary integral operators for domains with unbounded smooth boundary

  • Vladimir Rabinovich EMAIL logo
Published/Copyright: October 25, 2016
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Abstract

The paper is devoted to the Lp-theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spaces Hs,p(D), p(1,), and the Besov spaces Bp,qs(D), p,q[1,]. We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.

MSC 2010: 35J25; 35Q60

Dedicated to the memory of Academician Nikoloz Muskhelishvili on the occasion of his 125th birthday anniversary


Award Identifier / Grant number: CB-179872-F

Funding statement: Partially supported by the CONACYT project CB-179872-F.

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Received: 2016-8-10
Accepted: 2016-9-20
Published Online: 2016-10-25
Published in Print: 2016-12-1

© 2016 by De Gruyter

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