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Elliptic equations in the plane satisfying a Carleson measure condition

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Original languageEnglish
Pages (from-to)1013-1034
Number of pages22
JournalRevista Matemática Iberoamericana
Volume26
Issue number3
Publication statusPublished - 2010

Abstract

In this paper we settle (in dimension n, = 2) the open question whether for a divergence form equation div(A del u) = 0 with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the L-p Neumann and Dirichlet regularity problems are solvable for some values of p is an element of (1, infinity). The related question for the L-p Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].

    Research areas

  • elliptic equations, Carleson measure condition, Neumann problem, regularity problem, distributional inequalities, inhomogeneous equation

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