Abstract:This is a brief historical overview 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.

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中文翻译：

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椭圆和抛物线方程理论中的卢比奥·德·弗朗西亚外推定理和相关主题。一项调查

摘要：这是对线性椭圆和抛物线方程的Sobolev混合范数理论的简要历史回顾，以及基于Rubio de Francia外推定理的该理论的最新发展。还介绍了该定理的独立证明以及Real Analysis的其他相关工具，以及在完全非线性方程的混合范数估计中的应用。

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