Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindoš; David J. Rule

Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindoš, David J. Rule

Research output: Contribution to journal › Article › peer-review

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 L^P Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].

Original language	English
Pages (from-to)	1013-1034
Number of pages	22
Journal	Revista Matemática Iberoamericana
Volume	26
Issue number	3
Publication status	Published - 2010

Keywords

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

Cite this

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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].",

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AU - Rule, David J.

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AB - 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].

KW - Carleson measure condition

KW - Distributional inequalities

KW - Elliptic equations

KW - Inhomogeneous equation

KW - Neumann problem

KW - Regularity problem

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Elliptic equations in the plane satisfying a Carleson measure condition

Abstract

Keywords

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