一类平均曲率方程的内部梯度估计
Internal Gradient Estimation for a Class of Mean Curvature Equations
摘要: 本文研究了一类平均曲率方程,通过选取适当的辅助函数G,然后运用极值原理和对极值点性质的讨论,得到了此类平均曲率方程的内部梯度估计,完善了此类方程的内部梯度估计。
Abstract: In this paper, we study a class of mean curvature equations. By selecting an appropriate auxiliary function G, and then using the extreme value principle and the discussion of the properties of ex-treme points, we obtain the internal gradient estimation of such mean curvature equations, and improve the internal gradient estimation of such equations.
文章引用:司雨欣, 韩菲, 孙文静. 一类平均曲率方程的内部梯度估计[J]. 理论数学, 2022, 12(11): 1910-1917. https://doi.org/10.12677/PM.2022.1211205

参考文献

[1] Bombieri, E., De Giorgi, E. and Miranda, M. (1969) Una maggiorazone a priori relativa alleipersuperfici minimali non parabolic. Archive for Rational Mechanics and Analysis, 32, 255-267. [Google Scholar] [CrossRef
[2] Ladyzhenskaya, O.A. and Ural’Tseva, N.N. (1970) Local Estimates for Solution of Non-Uniformly Elliptic and Para- bolic Equations. Communications on Pure and Applied Mathematics, 23, 677-703. [Google Scholar] [CrossRef
[3] Gilbarg, D. and Trudinger, N.S. (2001) Elliptic Partial Differential Equation of Second Order. Springer-Verlag, Berlin. [Google Scholar] [CrossRef
[4] Barles, G. (1991) Interior Gradient Bounds for the Mean Curva-ture Equation by Viscosity Solutions Methods. Differential Integral Equations, 4, 263-275.
[5] Wang, X.J. (1998) Interior Gradient Estimates for Mean Curvature Equations. Mathematische Zeitschrift, 228, 73-81. [Google Scholar] [CrossRef
[6] Ma, X. and Xu, J. (2016) Gradient Estimates of Mean Curvature Equa-tions with Neumann Boundary Value Problems. Advances in Mathematics, 290, 1010-1039. [Google Scholar] [CrossRef
[7] 麻希南, 王培合. 具有给定Neumann边值或预定夹角边值的平均曲率方程的边界梯度估计[J]. 中国科学: 数学, 2018, 48(1): 213-226.
[8] 王聪涵. 平均曲率型方程的内部梯度估计和Liouville型结果[D]: [硕士学位论文]. 新乡: 河南师范大学, 2019.