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Pure Mathematics 2020
一类散度型椭圆方程的霍普夫引理
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Abstract:
极值原理是椭圆偏微分方程的基本性质之一,线性椭圆偏微分方程具有强极值原理,其证明依赖于霍普夫引理。本文得到一类散度型椭圆方程的霍普夫引理。
The Maximum Principle is one of the basic properties of elliptic partial differential equations. Linear elliptic partial differential equations have strong maximum principle, whose proof depends on Hopf’s lemma. This paper obtains Hopf’s lemma for a class of divergence elliptic equations.
[1] | 保继光, 朱汝金. 偏微分方程[M]. 北京: 北京师范大学出版社, 2011: 120. |
[2] | Han, Q. and Lin, F.H. (2011) El-liptic Partial Differential Equations. American Mathematical Society, 21-27. |
[3] | Finn, R. and Gilbarg, D. (1957) Asymptotic Behavior and Uniqueness of Plane Subsonic Flows. Communications on Pure and Applied Mathematics, 10, 23-63. https://doi.org/10.1002/cpa.3160100102 |
[4] | de Lis, S. and José, C. (2015) Hopf Maximum Principle Revisited. Electronic Journal of Differential Equations, 115, 1-9. |
[5] | Gilbarg, D. and Trudinger, N.S. (1983) Elliptic Partial Differential Equations of Second Order. Springer Verlag. |