Poisson方程与热传导方程的加权 Lp估计
Weighted Lp Estimates for the Poisson Equation and Heat Equation
摘要: Poisson方程与热传导方程的Lp估计是最基本的正则性估计。本文我们主要研究Poisson方程与热传导方程的一类新的正则性估计–加权Lp估计。
Abstract: Lp estimates for the Poisson equation and heat equation are the most basic regularity estimates. In this paper, we mainly study a new class of regularity estimates, weighted Lp estimates, for the Poisson equation and heat equation.
文章引用：苗钱. Poisson方程与热传导方程的加权 Lp估计[J]. 理论数学, 2013, 3(3): 207-214. http://dx.doi.org/10.12677/PM.2013.33031

参考文献

[1] L. Wang. A geometric approach to the Calderon-Zygmund estimates. Acta Mathematica Sinica (English Series), 2003, 19(2): 381-396.
[2] L. A. Caffarelli, I. Peral. On estimates for elliptic equations in divergence form. Communications on Pure and Applied Mathematics, 1998, 51(1): 1-21.
[3] S. Byun, L. Wang. Elliptic equations with BMO coefficients in Reifenberg domains. Communications on Pure and Applied Mathematics, 2004, 57(10): 1283-1310.
[4] S. Byun, L. Wang. estimates for parabolic equations in Reifenberg domains. Journal of Functional Analysis, 2005, 223(1): 44-85.
[5] S. Byun, L. Wang. Parabolic equations in Reifenberg domains. Archive for Rational Mechanics and Analysis, 2005, 176: 271-301.
[6] S. Byun, L. Wang. Parabolic equations in time dependent Reifenberg domains. Advances in Mathematics, 2007, 212(2): 797-818.
[7] S. Byun, L.Wang. Quasilinear elliptic equations with BMO coefficients in Lipschitz domains. Transactions of the American Mathematical Society, 2007, 359(12): 5899-5913.
[8] T. Mengesha, N. Phuc. Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains. Journal of Differential Equations, 2011, 250(5): 2485-2507.
[9] T. Mengesha, N. Phuc. Global estimates for quasilinear elliptic equations on Reifenberg flat domains. Archive for Rational Mechanics and Analysis, 2012, 203(1): 189-216.
[10] E. M. Stein. Harmonic analysis. Princeton: Princeton University Press, 1993.
[11] 周民强. 调和分析讲义(实变函数)[M]. 北京: 北京大学出版社, 2003.
[12] E. Acerbi, G. Mingione. Gradient estimates for a class of parabolic systems. Duke Mathematical Journal, 2007, 136: 285-320.
[13] S. Byun, F. Yao and S. Zhou. Gradient estimates in Orlicz space for nonlinear elliptic equations. Journal of Functional Analysis, 2008, 255(8): 1581-1873.
[14] L. Wang, F. Yao, S. Zhou and H. Jia. Optimal regularity for the Poisson equation. Proceedings of the American Mathematical Society, 2009, 137(6): 2037-2047.
[15] Y. Chen, L. Wu. Second order elliptic partial differential equations and elliptic systems. Providence: American Mathematical Society, 1998.
[16] M. Giquinta. Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton: Princeton University Press, 1983.

为你推荐