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September, 2010 Elliptic equations in the plane satisfying a Carleson measure condition
Martin Dindoš , David J. Rule
Rev. Mat. Iberoamericana 26(3): 1013-1034 (September, 2010).


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].


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Martin Dindoš . David J. Rule . "Elliptic equations in the plane satisfying a Carleson measure condition." Rev. Mat. Iberoamericana 26 (3) 1013 - 1034, September, 2010.


Published: September, 2010
First available in Project Euclid: 27 August 2010

zbMATH: 1206.35101
MathSciNet: MR2789374

Primary: 35J25
Secondary: 35J67

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

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid


Vol.26 • No. 3 • September, 2010
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