Revista Matemática Iberoamericana
- Rev. Mat. Iberoamericana
- Volume 26, Number 3 (2010), 1013-1034.
Elliptic equations in the plane satisfying a Carleson measure condition
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].
Rev. Mat. Iberoamericana, Volume 26, Number 3 (2010), 1013-1034.
First available in Project Euclid: 27 August 2010
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Dindoš, Martin; Rule, David J. Elliptic equations in the plane satisfying a Carleson measure condition. Rev. Mat. Iberoamericana 26 (2010), no. 3, 1013--1034. https://projecteuclid.org/euclid.rmi/1282913830