Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindoš, David J. Rule

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper we settle (in dimension n = 2) the open question whether for a divergence form equation div(A?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 e (1, 8). The related question for the LP Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].

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


  • Carleson measure condition
  • Distributional inequalities
  • Elliptic equations
  • Inhomogeneous equation
  • Neumann problem
  • Regularity problem


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