The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients |
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| Authors: | Vladimir Maz’ya Marius Mitrea Tatyana Shaposhnikova |
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| Institution: | 1.Department of Mathematics,Ohio State University,Columbus,USA;2.Department of Mathematical Sciences,University of Liverpool,Liverpool,UK;3.Department of Mathematics,Link?ping University,Link?ping,Sweden;4.Department of Mathematics,University of Missouri at Columbia,Columbia,USA |
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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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