Revista Matemática Iberoamericana

Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindoš and David J. Rule

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In this paper we settle (in dimension $n=2$) the open question whether for a divergence form equation $\div (A\nabla u) = 0$ 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 $p\in (1,\infty)$. The related question for the $L^p$ 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].

Article information

Rev. Mat. Iberoamericana, Volume 26, Number 3 (2010), 1013-1034.

First available in Project Euclid: 27 August 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35J67: Boundary values of solutions to elliptic equations

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


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

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