Аннотация:
This is a brief overview of the history of the Sobolev mixed norm theory of linear elliptic and parabolic equations and the recent development in this theory based on the Rubio de Francia extrapolation theorem. A self contained proof of this theorem along with other relevant tools of Real Analysis are also presented as well as an application to mixed norm estimates for fully nonlinear equations.
Ключевые слова:
Rubio de Francia extrapolation theorem, mixed norm estimates.
Образец цитирования:
N. V. Krylov, “Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey”, Алгебра и анализ, 32:3 (2020), 5–38; St. Petersburg Math. J., 32:3 (2021), 389–413
\RBibitem{Kry20}
\by N.~V.~Krylov
\paper Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A~survey
\jour Алгебра и анализ
\yr 2020
\vol 32
\issue 3
\pages 5--38
\mathnet{http://mi.mathnet.ru/aa1698}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 3
\pages 389--413
\crossref{https://doi.org/10.1090/spmj/1653}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1698
https://www.mathnet.ru/rus/aa/v32/i3/p5
Эта публикация цитируется в следующих 8 статьяx:
Pascal Auscher, Pierre Portal, “Stochastic and deterministic parabolic equations with bounded measurable coefficients in space and time: Well-posedness and maximal regularity”, Journal of Differential Equations, 420 (2025), 1
Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko, Operator Theory: Advances and Applications, 298, Integral Operators in Non-Standard Function Spaces, 2024, 247
Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko, Operator Theory: Advances and Applications, 298, Integral Operators in Non-Standard Function Spaces, 2024, 57
Jae-Hwan Choi, “A Regularity Theory for Evolution Equations with Time-measurable Pseudo-differential Operators in Weighted Mixed-norm Sobolev-Lipschitz Spaces”, Potential Anal, 2024
Hong Tian, Shenzhou Zheng, “Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of p-growth”, Rocky Mountain J. Math., 52:2 (2022)
Timothy Robertson, “Wellposedness of Keller-Segel systems in mixed norm spaces”, ejde, 2022, no. Conference 26, 139
Hongjie Dong, Timur Yastrzhembskiy, “Global Lp Estimates for Kinetic Kolmogorov–Fokker–Planck Equations in Nondivergence Form”, Arch Rational Mech Anal, 245:1 (2022), 501
Tuoc Phan, Robertson T., “On Masuda uniqueness theorem for Leray-Hopf weak solutions in mixed-norm spaces”, Eur. J. Mech. B-Fluids, 90 (2021), 18–28
Цитирование в формате AMSBIB
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