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Spectral properties for layer potentials associated to the Stokes equation in Lipschitz domains

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Abstract

In this paper, we consider the spectral properties of the double layer potentials K and \({\tilde{K}}\) related to the traction boundary value problem and the slip boundary value problem, respectively, of the Stokes equations in a bounded Lipschitz domain Ω in R n. We show the invertibility of λI − K and \({\lambda I - \tilde{K}}\) in L 2(∂Ω) for \({\lambda \in {\bf R}{\setminus} [-\frac 12, \frac12]}\). As an application, we study the transmission problems of the Stokes equations.

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Authors and Affiliations

  1. Department of Mathematics of KIAS, Korea Institute for Advanced Study, Seoul, 130-722, Korea

    Tong Keun Chang

  2. Department of Mathematics, Yonsei University, Seodaemun-gu, Seoul, Republic of Korea

    Dae Hyeon Pahk

Authors
  1. Tong Keun Chang
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  2. Dae Hyeon Pahk
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Correspondence to Tong Keun Chang.

Additional information

D. H. Pahk is supported by the Korea Research Grant Foundation KRF-2005-015-C00036.

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Chang, T.K., Pahk, D.H. Spectral properties for layer potentials associated to the Stokes equation in Lipschitz domains. manuscripta math. 130, 359–373 (2009). https://doi.org/10.1007/s00229-009-0292-1

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  • DOI: https://doi.org/10.1007/s00229-009-0292-1

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