ESTIMATES OF GREEN FUNCTIONS AND HARMONIC MEASURES FOR ELLIPTIC OPERATORS WITH SINGULAR DRIFT TERMS

In this paper, we prove the existence and uniqueness of the continuous Green function G for the elliptic operator L = div(A(x)∇x) + B(x)· ∇x with singular drift term B on a C1,1 bounded domain D in ℝn, n ≥ 3, and its comparability to the Green function G₀ of L₀ = div(A(x) ∇x). Basing on this result...

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Bibliographic Details
Published inPublicacions matemàtiques Vol. 49; no. 1; pp. 159 - 177
Main Authors Ifra, Abdoul, Riahi, Lotfi
Format Journal Article
LanguageEnglish
Published Universitat Autònoma de Barcelona 01.01.2005
Subjects
Equivalence relation
Greens function
Mathematical functions
Mathematical inequalities
Mathematical theorems
Potential theory
Singular terms
Uniqueness
Vector fields
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Summary:In this paper, we prove the existence and uniqueness of the continuous Green function G for the elliptic operator L = div(A(x)∇x) + B(x)· ∇x with singular drift term B on a C1,1 bounded domain D in ℝn, n ≥ 3, and its comparability to the Green function G₀ of L₀ = div(A(x) ∇x). Basing on this result we establish the equivalence of the L-harmonic measure and the surface measure on ∂D. These results extend some first ones proved for elliptic operators with less singular drift terms.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_49105_07