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Partial Differential Equations and Functional Analysis pp 113–121Cite as

On the Equation div u = g and Bogovskii’s Operator in Sobolev Spaces of Negative Order

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 168))

Abstract

Consider the divergence problem with homogeneous Dirichlet data on a Lipschitz domain. Two approaches for its solutions in the scale of Sobolev spaces are presented. The first one is based on Calderón-Zygmund theory, whereas the second one relies on the Stokes equation with inhomogeneous data.

The first author was financially supported by the DFG-Graduiertenkolleg 853, TU Darmstadt. The second author was financially supported by the JSPS.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, D-64289, Darmstadt, Germany

    Matthias Geißert, Horst Heck & Matthias Hieber

Authors
  1. Matthias Geißert
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  2. Horst Heck
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  3. Matthias Hieber
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Editor information

Editors and Affiliations

  1. Technische Universiteit Delft DIAM, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Erik Koelink , Jan van Neerven , Ben de Pagter  & Guido Sweers , ,  & 

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10 / 101, 1040, Wien, Austria

    Annemarie Luger  & Harald Woracek  & 

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Dedicated to Philippe Clément on the occasion of his retirement

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Geißert, M., Heck, H., Hieber, M. (2006). On the Equation div u = g and Bogovskii’s Operator in Sobolev Spaces of Negative Order. In: Koelink, E., van Neerven, J., de Pagter, B., Sweers, G., Luger, A., Woracek, H. (eds) Partial Differential Equations and Functional Analysis. Operator Theory: Advances and Applications, vol 168. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7601-5_7

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