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Journal d'Analyse Mathématique

, Volume 110, Issue 1, pp 167–239 | Cite as

The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients

  • Vladimir. Maz’yaEmail author
  • Marius Mitrea
  • Tatyana Shaposhnikova
Article

Abstract

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.

Keywords

Dirichlet Problem Lipschitz Function Boundary Data Elliptic System Besov Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  • Vladimir. Maz’ya
    • 1
    • 2
    • 3
    Email author
  • Marius Mitrea
    • 4
  • Tatyana Shaposhnikova
    • 1
    • 3
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  3. 3.Department of MathematicsLinköping UniversityLinköpingSweden
  4. 4.Department of MathematicsUniversity of Missouri at ColumbiaColumbiaUSA

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