理论数学  >> Vol. 4 No. 5 (September 2014)

热传导方程解的Schauder估计
Schauder Estimates for the Solutions of the Heat Equation

DOI: 10.12677/PM.2014.45030, PDF, HTML, 下载: 2,536  浏览: 5,957 

作者: 陈雯雯:上海大学理学院,上海

关键词: 紧方法热传导方程抛物Schauder估计Compactness Method Heat Equation Parabolic Schauder Estimates

摘要: 本文主要通过一种类似于紧方法的新方法来研究热传导方程解的Schauder估计。
Abstract: In this paper we study Schauder estimates for the solutions of the heat equation by a new method similar to the compactness method.

文章引用: 陈雯雯. 热传导方程解的Schauder估计[J]. 理论数学, 2014, 4(5): 208-217. http://dx.doi.org/10.12677/PM.2014.45030

参考文献

[1] Schauder, J. (1934) Uber lineare elliptische Differentialgleichungen zweiter Ordnung. Mathematische Zeitschrift, 38, 257-282.
[2] Schauder, J. (1934) Numerischen Abschadtzungen in elliptische lineare Differentialgleichungen. Studia Mathematica, 5, 34- 42.
[3] Campanato, S. (1964) Propriet di una famiglia di spazi funzionali. Annali della Scuola Normale Superiore di Pisa, 18, 137-160.
[4] Trudinger, N. (1986) A new approach to the Schauder estimates for linear elliptic equations. Proceedings of the Centre for Mathematical Analysis, Australian National University, 14, 52-59.
[5] Caffarelli, L. (1989) Interior a priori estimates for solutions of fully nonlinear equations. Annals of Ma-thematics, 130, 189-213.
[6] Ciliberto, C. (1954) Formule di maggiorazione e teoremi di esistenza per le soluzioni delle equazioni paraboliche in due variabili. Ricerche di Matematica, 3, 40-75.
[7] Han, Q. (2000) Schauder estimates for elliptic operators with applications to nodal sets. The Journal of Geometric Analysis, 10, 455-480.
[8] Simon, L. (1997) Schauder estimates by scaling. Calculus of Variations and Partial Differential Equations, 5, 391-407.
[9] Wang, L. (1994) Compactness methods for certain degenerate elliptic equations. Journal of Differential Equations, 107, 341-350.
[10] Wang, L. (2003) Holder estimates for subelliptic operators. Journal of Functional Analysis, 199, 228-242.
[11] Wang, L. Regularity Theory for Elliptic Equations. Preprint.
[12] Wang, X. (2006) Schauder estimates for elliptic and parabolic equations. Chinese Annals of Mathematics, Series B, 27, 637-642.
[13] Evans, L. (1998) Partial differential equations. In: Graduates Studies in Mathematics, American Mathematical Society, Providence, Vol. 19.