Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindos, David J. Rule

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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].

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

Keywords / Materials (for Non-textual outputs)

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


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