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- W4362470810 abstract "We study a class of non-divergence form elliptic and parabolic equations with singular first-order coefficients in an upper half space with the homogeneous Dirichlet boundary condition. In the simplest setting, the operators in the equations under consideration appear in the study of fractional heat and fractional Laplace equations. Intrinsic weighted Sobolev spaces are found in which the existence and uniqueness of strong solutions are proved under certain smallness conditions on the weighted mean oscillations of the coefficients in small parabolic cylinders. Our results are new even when the coefficients are constants and they cover the case where the weights may not be in the Ap-Muckenhoupt class." @default.
- W4362470810 created "2023-04-05" @default.
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- W4362470810 date "2023-07-01" @default.
- W4362470810 modified "2023-09-26" @default.
- W4362470810 title "Weighted mixed-norm L estimates for equations in non-divergence form with singular coefficients: The Dirichlet problem" @default.
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- W4362470810 doi "https://doi.org/10.1016/j.jfa.2023.109964" @default.
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