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Schauder Estimates for Elliptic and Parabolic Equations 被引量：7

Schauder Estimates for Elliptic and Parabolic Equations
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摘要 在这笔记，作者为椭圆形、抛物线的方程为 Schauderestimates 给一个基本、简单的证明。证明也适用于非线性的方程。 In this note the author gives an elementary and simple proof for the Schauder estimates for elliptic and parabolic equations. The proof also applies to nonlinear equations.
作者 Xu-Jia WANG
机构地区 Centre for Mathematics and its Applications
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第6期637-642,共6页 数学年刊（B辑英文版）
基金 Project supported by the Australian Research Council and the National Natural Science Foundation of China (No.10428103).
关键词 SCHAUDER估计 椭圆方程 抛物线方程 数学分析 偏微分方程 Schauder estimate, Elliptic equation, Parabolic equation
分类号 O175.2 [理学—基础数学]
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参考文献19

  • 1Burch, C., The Dini condition and regularity of weak solutions of elliptic equations, J. Differential Equations, 30, 1978, 308- 323.
  • 2Caffarelli, L. A., Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math. (2),130, 1989, 189 -213.
  • 3Caffarelli, L. A., Interior W^2,p estimates for solutions of Monge-Ampère equations, Ann. of Math. (2),131, 1990, 135- 150.
  • 4Caffarelli, L. A. and Cabre, X., Fully Nonlinear Elliptic Equations, Colloquium Pubblications, Vol. 43, A.M. S., Providence, RI, 1995.
  • 5Camnpanato, S., Propriet di una famiglia di spazi funzionali, Ann. Sc. Norm. Super Pisa Cl. Sci. (3), 18,1964, 137-160.
  • 6Evans, L. C., Classical solutions of fully nonlinear, convex, second order elliptic equations, Comm. Pure Appl. Math., 25, 1982, 333-363.
  • 7Evans, L. C., Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, A. M. S., Providence, RI, 1998.
  • 8Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer, 1983.
  • 9Kovats, J., Fully nonlinear elliptic equations and the Dini condition, Comm. Partial Differential Equations,22(11-12), 1997, 1911-1927.
  • 10Krylov, N. V., Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk. SSSR Set.Mat., 46, 1982, 487-523; English translation in Math. USSR Izv., 20, 1983, 459-492.

同被引文献6

引证文献7

二级引证文献10

Chinese Annals of Mathematics,Series B
2006年 第6期

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