Elliptic equations in the plane satisfying a Carleson measure condition

Martin Dindos; David J. Rule

Elliptic equations in the plane satisfying a Carleson measure condition

School of Mathematics

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 del 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 is an element of (1, infinity). 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 / Materials (for Non-textual outputs)

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

Access to Document

Elliptic equations in the plane satisfying a Carleson measure conditionAccepted author manuscript, 197 KB

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rmi/1282913830

Cite this

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title = "Elliptic equations in the plane satisfying a Carleson measure condition",

abstract = "In this paper we settle (in dimension n, = 2) the open question whether for a divergence form equation div(A del 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 is an element of (1, infinity). The related question for the L-p Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].",

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T1 - Elliptic equations in the plane satisfying a Carleson measure condition

AU - Dindos, Martin

AU - Rule, David J.

PY - 2010

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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 del 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 is an element of (1, infinity). The related question for the L-p Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].

KW - elliptic equations

KW - Carleson measure condition

KW - Neumann problem

KW - regularity problem

KW - distributional inequalities

KW - inhomogeneous equation

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JO - Revista Matemática Iberoamericana

JF - Revista Matemática Iberoamericana

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ER -

Elliptic equations in the plane satisfying a Carleson measure condition

Abstract

Keywords / Materials (for Non-textual outputs)

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Other files and links

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Solving partial differential equations and systems by techniques of harmonic analysis.

Centre for analysis and nonlinear differential equations

Cite this

Elliptic equations in the plane satisfying a Carleson measure condition

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Projects

Solving partial differential equations and systems by techniques of harmonic analysis.

Centre for analysis and nonlinear differential equations

Cite this