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Poisson-Transmission Problems for \(L^{\infty }\)-Perturbations of the Stokes System on Lipschitz Domains in Compact Riemannian Manifolds

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Abstract

The purpose of this work is to show the well-posedness in \(L^2\)-Sobolev spaces for a Poisson-transmission problem involving \(L^{\infty }\)-perturbations of the Stokes system on complementary Lipschitz domains in compact Riemannian manifolds. The technical details rely on the layer potential theory for the Stokes system and the invertibility of some perturbed zero index Fredholm operators by suitable compact operators. The compact part is provided by the \(L^{\infty }\)-perturbations of the Stokes system. An existence result for a related semilinear Poisson-transmission problem is also formulated.

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Acknowledgments

The work of Mirela Kohr and Cornel Pintea was supported by a grant of the Romanian National Authority for Scientific Research, CNCS—UEFISCDI, Project Number PN-II-ID-PCE-2011-3-0994.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084 , Cluj-Napoca, Romania

    Mirela Kohr & Cornel Pintea

  2. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring, 57, 70569 , Stuttgart, Germany

    Wolfgang L. Wendland

Authors
  1. Mirela Kohr
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  2. Cornel Pintea
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  3. Wolfgang L. Wendland
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Correspondence to Mirela Kohr.

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Dedicated to the memory of Klaus Kirchgässner.

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Kohr, M., Pintea, C. & Wendland, W.L. Poisson-Transmission Problems for \(L^{\infty }\)-Perturbations of the Stokes System on Lipschitz Domains in Compact Riemannian Manifolds. J Dyn Diff Equat 27, 823–839 (2015). https://doi.org/10.1007/s10884-014-9359-0

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  • DOI: https://doi.org/10.1007/s10884-014-9359-0

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