Small A∞ results for Dahlberg-Kenig-Pipher Operators in sets with uniformly rectifiable boundaries
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2023-11
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Journal Article
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Abstract
In the present paper we consider elliptic operators L = − div(A∇) in a domain bounded by a chord-arc surface Γ with small enough constant, and whose coefficients A satisfy a weak form of the Dahlberg-Kenig-Pipher condition of approximation by constant coefficient matrices, with a small enough Carleson norm, and show that the elliptic measure with pole at infinity associated to L is A∞-absolutely continuous with respect to the surface measure on Γ, with a small A∞ constant. In other words, we show that for relatively flat uniformly rectifiable sets and for operators with slowly oscillating coefficients the elliptic measure satisfies the A∞ condition with a small constant and the logarithm of the Poisson kernel has small oscillations.
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376 (11)
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7857 - 7909
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American Mathematical Society
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09774 - Mayboroda, Svitlana / Mayboroda, Svitlana