Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindoš, David J. Rule

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume26
Issue number3
Publication statusPublished - 2010

Keywords

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

Fingerprint Dive into the research topics of 'Elliptic equations in the plane satisfying a Carleson measure condition'. Together they form a unique fingerprint.

Cite this