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Nonlinear Neumann–Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains

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Abstract

The purpose of this paper is to use a layer potential analysis and the Leray–Schauder degree theory to show an existence result for a nonlinear Neumann–transmission problem corresponding to the Stokes and Brinkman operators on Euclidean Lipschitz domains with boundary data in L p spaces, Sobolev spaces, and also in Besov spaces.

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Authors and Affiliations

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

    Mirela Kohr

  2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, Padova, 35121, Italy

    Massimo Lanza de Cristoforis

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

    Wolfgang L. Wendland

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  1. Mirela Kohr
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  2. Massimo Lanza de Cristoforis
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  3. Wolfgang L. Wendland
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Kohr, M., Lanza de Cristoforis, M. & Wendland, W.L. Nonlinear Neumann–Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains. Potential Anal 38, 1123–1171 (2013). https://doi.org/10.1007/s11118-012-9310-0

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