JournalsrmiVol. 26, No. 3pp. 1013–1034

Elliptic equations in the plane satisfying a Carleson measure condition

  • Martin Dindoš

    Edinburgh University, UK
  • David J. Rule

    Heriot-Watt University, Edinburgh, UK
Elliptic equations in the plane satisfying a Carleson measure condition cover
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Abstract

In this paper we settle (in dimension n=2n=2) the open question whether for a divergence form equation ÷(Au)=0\div (A\nabla u) = 0 with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the LpL^p Neumann and Dirichlet regularity problems are solvable for some values of p(1,)p\in (1,\infty). The related question for the LpL^p Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [Kenig, C.E. and Pipher, J.: The Dirichlet problem for elliptic equations with drift terms. Publ. Mat. 45 (2001), no. 1, 199-217].

Cite this article

Martin Dindoš, David J. Rule, Elliptic equations in the plane satisfying a Carleson measure condition. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 1013–1034

DOI 10.4171/RMI/625