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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    Vladimir. Maz’ya & Tatyana Shaposhnikova

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, UK

    Vladimir. Maz’ya

  3. Department of Mathematics, Linköping University, Linköping, SE-581 83, Sweden

    Vladimir. Maz’ya & Tatyana Shaposhnikova

  4. Department of Mathematics, University of Missouri at Columbia, Columbia, MO, 65211, USA

    Marius Mitrea

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  1. Vladimir. Maz’ya
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  2. Marius Mitrea
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  3. Tatyana Shaposhnikova
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Correspondence to Vladimir. Maz’ya.

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The work of the authors was supported in part by NSF, DMS and FRG grants as well as the Swedish National Science Research Council.

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Maz’ya, V., Mitrea, M. & Shaposhnikova, T. The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients. JAMA 110, 167–239 (2010). https://doi.org/10.1007/s11854-010-0005-4

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  • DOI: https://doi.org/10.1007/s11854-010-0005-4

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