| A Note on the Maximum Principle for Second-Order Elliptic Equations in General Domains |
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| 引用本文： | Antonio VITOLO. A Note on the Maximum Principle for Second-Order Elliptic Equations in General Domains[J]. 数学学报(英文版), 2007, 23(11): 1955-1966. DOI: 10.1007/s10114-007-0976-y |
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| 作者姓名： | Antonio VITOLO |
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| 作者单位： | Department of Mathematics and Informatics, University of Salerno P. Grahamstown,84084 Fisciano （Salerno）, Italy |
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| 基金项目： | Supported by MURST ex 60% 2005-06 |
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| 摘 要： | ![]()
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| 关 键 词： | 椭圆型方程 偏微分方程 极大值原理 一般域 |
| 收稿时间： | 2005-04-15 |
| 修稿时间： | 2005-05-10 |
A Note on the Maximum Principle for Second-Order EllipticEquations in General Domains |
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| Antonio Vitolo. A Note on the Maximum Principle for Second-Order EllipticEquations in General Domains[J]. Acta Mathematica Sinica(English Series), 2007, 23(11): 1955-1966. DOI: 10.1007/s10114-007-0976-y |
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| Authors: | Antonio Vitolo |
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| Affiliation: | (1) Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611-8105, USA |
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| Abstract: | ![]()
We make a further advance concerning the maximum principle for second-order elliptic operators. We investigate in particular a geometric condition, first considered by Berestycki Nirenberg Varadhan, that seems to be natural in view of the application of the boundary weak Harnack inequality, on which our argument is based. Setting it free from some technical assumptions, apparently needed in earlier papers, we significantly enlarge the class of unbounded domains where the maximum principle holds, compatibly with the first-order term. |
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| Keywords: | elliptic equations ABP estimate maximum principle |
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