The Dirichlet problem for elliptic equations in divergence and nondivergence form with singular drift term
Analysis of PDEs
2007-05-23 v1
Abstract
Given two elliptic operators L and M in nondivergence form, with coefficients A_L(x), A_M(x) and drift terms b_L(x), b_M(x), respectively, satisfying a Carleson measure disagreement condition in a Lipschitz domain Omega in R^{n+1}, then their harmonic measures are mutually absolutely continuous. As an application of this, a new approximation argument and known results we obtain necessary and sufficient conditions for a single operator L (in divergence or nondivergence form) to have regular harmonic measure with respect to Lebesgue measure. The results are sharp in all cases.
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Cite
@article{arxiv.math/0510393,
title = {The Dirichlet problem for elliptic equations in divergence and nondivergence form with singular drift term},
author = {Cristian Rios},
journal= {arXiv preprint arXiv:math/0510393},
year = {2007}
}
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29 pages, 0 figures