Laplace方程的斜导数边值问题梯度估计
The Gradient Estimation of Oblique Derivative Boundary Value Problems for Laplace Equation
摘要: 本文主要是研究一类Laplace方程第二边值问题的梯度估计，通过构造合适的辅助函数，利用函数在极大值点的性质，证明Laplace方程的斜导数边值问题解的梯度估计，得到了一类带Du的Laplace方程第二类边值问题解的全局梯度估计。
Abstract:
In this paper, we study the gradient estimation of the second boundary value problem for a class of Laplace equations. By constructing appropriate auxiliary functions and using the properties of functions at maximum points, we prove the gradient estimation of the solution of the oblique de-rivative boundary value problem for the Laplace equation, and obtain the global gradient estima-tion of the solution of the second class boundary value problem for the Laplace equation with Du.
参考文献
|
[1]
|
Serrn, J. (1969) The Problem of Dirichlet for Quasilinear Elliptic Differential Equations with Many Independent Vari-ables. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 264, 413-496. [Google Scholar] [CrossRef]
|
|
[2]
|
Gilbarg, D., Trudinger, N.S., Gilbarg, D., et al. (2001) El-liptic Partial Differential Equations of Second Order. Springer, New York. [Google Scholar] [CrossRef]
|
|
[3]
|
Xu, J.J. (2014) Gradient Estimates for the Neumann Problem of Mean Curvature Equation. Ph.D. Thesis, University of Science and Technology of China, Hefei.
|
|
[4]
|
Spruck, J. (1975) On the Existence of a Capillary Surface with Prescribed Contact Angle. Communications on Pure and Applied Math-ematics, 28, 189-200. [Google Scholar] [CrossRef]
|
|
[5]
|
Wang, X.J. (1998) Interior Gradient Estimates for Mean Curvature Equations. Mathematische Zeitschrift, 228, 73-82. [Google Scholar] [CrossRef]
|
|
[6]
|
Liberman, G.M. (1984) The Nonlinear Oblique Derivative Problems for Quasilinear Elliptic Equations. Nonlinear Analysis: Theory, Methods & Applications, 8, 49-65. [Google Scholar] [CrossRef]
|
|
[7]
|
向妮, 石菊花, 徐金菊, 吴燕. Laplace方程斜边值问题的梯度估计[J]. 数学物理学报, 2016, 36(3): 481-492.
|