双调和抛物方程解的局部Lorentz估计
Local Lorentz Estimates for the Bi-Harmonic Parabolic Equation
摘要: Lp估计是偏微分方程中基本的正则性估计，本文我们主要研究一类四阶双调和抛物方程的解的新的正则性估计——Lorentz估计。
Abstract: Lp estimates are the basic regularity estimates in the partial differential equations. In this paper, we mainly study a new class of regularity estimates—Lorentz estimates for the Bi-harmonic parabolic equation.
文章引用：朱加义. 双调和抛物方程解的局部Lorentz估计[J]. 理论数学, 2019, 9(5): 601-610. https://doi.org/10.12677/PM.2019.95080

参考文献

[1] Wang, L. (2003) A Geometric Approach to the Calderón-Zygmund Estimates. Acta Mathematica Sinica, 19, 381-396.
[Google Scholar] [CrossRef] 
[2] Caffarelli, L. and Peral, I. (1998) On Estimates for Elliptic Equations in Divergence Form. Communications on Pure and Applied Mathematics, 51, 1-21.
[Google Scholar] [CrossRef] 
[3] Byun, S. and Wang, L. (2004) Elliptic Equations with BMO Coefficients in Reifenberg Domains. Communications on Pure and Applied Mathematics, 57, 1283-1310.
[Google Scholar] [CrossRef] 
[4] Byun, S. and Wang, L. (2005) Estimates for Parabolic Equations in Reifenberg Domains. Journal of Functional Analysis, 223, 44-85.
[Google Scholar] [CrossRef] 
[5] Byun, S. and Wang, L. (2005) Parabolic Equations in Reifenberg Domains. Archive for Rational Mechanics and Analysis, 176, 271-301.
[Google Scholar] [CrossRef] 
[6] Byun, S. and Wang, L. (2007) Parabolic Equations in Time Dependent Rei-fenberg Domains. Advances in Mathematics, 212, 797-818.
[Google Scholar] [CrossRef] 
[7] Byun, S. and Wang, L. (2007) Quasilinear Elliptic Equations with BMO Coefficients in Lipschitz Domains. Transactions of the American Mathematical Society, 359, 5899-5913.
[Google Scholar] [CrossRef] 
[8] Baroni, P. (2013) Lorentz Estimates for De-generate and Singular Evolutionary Systems. Journal of Differential Equations, 255, 2927-2951.
[Google Scholar] [CrossRef] 
[9] Yao, F.P. and Zhou, S.L. (2008) Global Estimates for the Parabolic Equa-tions of the Bi-Harmonic Type. Journal of Partial Differential Equations, 21, 315-334.
[10] Yao, F.P. and Zhou, S.L. (2007) Schauder Estimates for the Bi-Harmonic Parabolic Equation. Applied Mathematics and Mechanics, 11, 1340-1352.
[Google Scholar] [CrossRef] 
[11] Yu, H.C. (2015) Weighted Estimates for the Bi-Harmonic Parabolic Equation. Pure Mathematics, 5, 46-53.
[Google Scholar] [CrossRef] 
[12] Hardy, G.H., Littlewood, J.E. and Polya, G. (1952) Inequalities. Cambridge University Press, Cambridge.
[13] Stein, E.M. (1970) Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ.
[Google Scholar] [CrossRef] 
[14] 伍卓群, 尹景学, 王春朋. 椭圆与抛物型方程引论[M]. 北京: 科学出版社, 2003.
[15] Mingione, G. (2007) The Calderón-Zygmund Theory for the Elliptic Problems with Measure Data. Annali della Scuola Normale Superiore di Pisa, 6, 195-261.

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