Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces

Wang L.; Yao F.

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Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces

机译：Sobolev空间和Orlicz空间中的高阶非散度椭圆和抛物方程

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摘要

In this paper we obtain the global regularity estimates of the solutions in Sobolev spaces and Orlicz spaces for higher-order elliptic and parabolic equations of nondivergence form in the whole space. We only need to focus on the parabolic case since the corresponding result in the elliptic case can be obtained as a corollary.

机译：在本文中，我们获得了Sobolev空间和Orlicz空间中整体空间的高阶椭圆型和抛物型方程的解的整体正则性估计。我们只需要关注抛物线情况，因为椭圆情况下的相应结果可以作为推论获得。

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《Journal of Functional Analysis》 |2012年第8期|共23页
作者
Wang L.; Yao F.;
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正文语种 eng
中图分类数学;
关键词
Elliptic; parabolic; Higher-order; Nondivergence; Orlicz spaces; Regularity; Small BMO; Sobolev; The whole space;

机译：椭圆;抛物线;高阶;不散度;Orlicz空间;正则性;小BMO;Sobolev;整个空间;

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专利

1. Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces [J] . Wang L., Yao F. Journal of Functional Analysis . 2012,第8期

机译：Sobolev空间和Orlicz空间中的高阶非散度椭圆和抛物方程
2. Global weighted estimates in Orlicz spaces for second-order nondivergence parabolic equations [J] . Yao Fengping Nonlinear Analysis: An International Multidisciplinary Journal . 2016,第Null期

机译：二阶非散度抛物型方程在Orlicz空间中的全局加权估计
3. Weighted estimates for nondivergence parabolic equations in Orlicz spaces [J] . Byun, Sun-Sig, Lee, Mikyoung Journal of Functional Analysis . 2015,第8期

机译：Orlicz空间中非散度抛物方程的加权估计
4. The regularity estimates for the solutions of general elliptic equations in Orlicz spaces [C] . Tao Xiangxing 2011 International Conference on E-Business and E-Government . 2011

机译：Orlicz空间中一般椭圆方程解的正则估计
5. Analysis of Nonlocal Equations: One-sided Weighted Fractional Sobolev Spaces and Harnack Inequality for Fractional Nondivergence Form Elliptic Equations [D] . ?Vaughan, Mary Colleen 2020

机译：非局部方程分析：片面加权分数索伯列夫空间和哈纳克不等式分数非散度型方程
6. EIGENFUNCTION EXPANSIONS FOR SINGULAR ELLIPTIC OPERATORS. II. THE HILBERT SPACE ARGUMENT; PARABOLIC EQUATIONS ON OPEN MANIFOLDS [O] . Felix E. Browder 1954

机译：奇异椭圆算子的本征函数展开式。二。希尔伯特空间论证；开流形上的抛物线方程
7. Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces [O] . Wang Lihe, Yao Fengping 2012

机译：Sobolev空间和Orlicz空间中的高阶非散度椭圆和抛物方程
8. Geometric approach to Sobolev spaces and badly degenerated elliptic equations [R] . Hajlasz, P. 1995

机译：sobolev空间和严重退化椭圆方程的几何方法

Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces

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