TY - JOUR
T1 - Carleson Measure Estimates for the Green Function
AU - David, Guy
AU - Li, Linhan
AU - Mayboroda, Svitlana
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.
PY - 2022/3
Y1 - 2022/3
N2 - In the present paper we consider an elliptic divergence form operator in the half-space and prove that its Green function is almost affine, or more precisely, that the normalized difference between the Green function and a suitable affine function at every scale satisfies a Carleson measure estimate, provided that the oscillations of the coefficients satisfy the traditional quadratic Carleson condition. The results are sharp, and in particular, it is demonstrated that the class of the operators considered in the paper cannot be improved.
AB - In the present paper we consider an elliptic divergence form operator in the half-space and prove that its Green function is almost affine, or more precisely, that the normalized difference between the Green function and a suitable affine function at every scale satisfies a Carleson measure estimate, provided that the oscillations of the coefficients satisfy the traditional quadratic Carleson condition. The results are sharp, and in particular, it is demonstrated that the class of the operators considered in the paper cannot be improved.
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U2 - 10.1007/s00205-021-01746-0
DO - 10.1007/s00205-021-01746-0
M3 - Article
AN - SCOPUS:85123930618
SN - 0003-9527
VL - 243
SP - 1525
EP - 1563
JO - Archive For Rational Mechanics And Analysis
JF - Archive For Rational Mechanics And Analysis
IS - 3
ER -