BMO Solvability and the A ∞ Condition for Elliptic Operators

Martin Dindos; Carlos Kenig; Jill Pipher

doi:10.1007/s12220-010-9142-3

BMO Solvability and the A _∞ Condition for Elliptic Operators

Martin Dindos, Carlos Kenig, Jill Pipher

School of Mathematics

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

Abstract

We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L-p solvability for all p > p(0).

Original language	English
Pages (from-to)	78-95
Number of pages	18
Journal	Journal of Geometric Analysis
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s12220-010-9142-3
Publication status	Published - Jan 2011

Keywords / Materials (for Non-textual outputs)

Dirichlet problem
Elliptic measure
Bounded mean oscillation
WEIGHTED NORM INEQUALITIES
DIRICHLET PROBLEM
MAXIMAL FUNCTIONS
HARDY-SPACES
EQUATIONS
DOMAINS
COEFFICIENTS
CONTINUITY
VARIABLES

Access to Document

10.1007/s12220-010-9142-3

BMO_solvability_and_the_A _condition_for_elliptic_operatorsAccepted author manuscript, 813 KB

http://link.springer.com/article/10.1007%2Fs12220-010-9142-3

Cite this

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title = "BMO Solvability and the A ∞ Condition for Elliptic Operators",

abstract = "We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L-p solvability for all p > p(0).",

keywords = "Dirichlet problem, Elliptic measure, Bounded mean oscillation, WEIGHTED NORM INEQUALITIES, DIRICHLET PROBLEM, MAXIMAL FUNCTIONS, HARDY-SPACES, EQUATIONS, DOMAINS, COEFFICIENTS, CONTINUITY, VARIABLES",

author = "Martin Dindos and Carlos Kenig and Jill Pipher",

year = "2011",

month = jan,

doi = "10.1007/s12220-010-9142-3",

language = "English",

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T1 - BMO Solvability and the A ∞ Condition for Elliptic Operators

AU - Dindos, Martin

AU - Kenig, Carlos

AU - Pipher, Jill

PY - 2011/1

Y1 - 2011/1

N2 - We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L-p solvability for all p > p(0).

AB - We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L-p solvability for all p > p(0).

KW - Dirichlet problem

KW - Elliptic measure

KW - Bounded mean oscillation

KW - WEIGHTED NORM INEQUALITIES

KW - DIRICHLET PROBLEM

KW - MAXIMAL FUNCTIONS

KW - HARDY-SPACES

KW - EQUATIONS

KW - DOMAINS

KW - COEFFICIENTS

KW - CONTINUITY

KW - VARIABLES

UR - https://www.scopus.com/pages/publications/79951513032

U2 - 10.1007/s12220-010-9142-3

DO - 10.1007/s12220-010-9142-3

M3 - Article

SN - 1050-6926

VL - 21

SP - 78

EP - 95

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -

BMO Solvability and the A _∞ Condition for Elliptic Operators

Abstract

Keywords / Materials (for Non-textual outputs)

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

Cite this

BMO Solvability and the A ∞ Condition for Elliptic Operators

Abstract

Keywords / Materials (for Non-textual outputs)

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Other files and links

Fingerprint

Projects

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

Cite this

BMO Solvability and the A _∞ Condition for Elliptic Operators