Neumann-transmission problems for pseudodifferential Brinkmanoperators on Lipschitz domains in compact Riemannian manifolds

Mirela Kohr; Cornel Pintea; Wolfgang L. Wendland

doi:10.3934/cpaa.2014.13.175

Article Contents

2014, Volume 13, Issue 1: 175-202. Doi: 10.3934/cpaa.2014.13.175

This issue Previous Article Asymptotic behaviour of the nonautonomous SIR equations with diffusion Next Article A pair of positive solutions for $(p,q)$-equations with combined nonlinearities

Neumann-transmission problems for pseudodifferential Brinkman operators on Lipschitz domains in compact Riemannian manifolds

1.
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084 Cluj-Napoca
2.
Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart

Received: September 30, 2012

Revised: March 31, 2013

Published: December 2013

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Abstract

The aim of this paper is twofold. On the one hand we construct Neumann-transmission kernels for pseudodifferential Brinkman operators. They are used to provide simple representations of the solution to some transmission problems for the pseudodifferential Brinkman operator. On the other hand, we show the well-posedness of a Neumann-transmission problem for two pseudodifferential Brinkman operators on adjacent Lipschitz domains in a compact Riemannian manifold, with boundary data in some $L^p$, Sobolev or Besov spaces. We rely on the layer potential theory in order to obtain an explicit representation of the solution to this problem. Compactness and invertibility results of associated layer potential operators on $L^p$, Sobolev and Besov spaces are also presented.

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Mathematics Subject Classification: Primary 35J25; Secondary: 42B20, 46E35, 76D, 76M.

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