| R^N中的非线性退化椭圆方程粘性解的存在性 |
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| 引用本文： | 项阳.R^N中的非线性退化椭圆方程粘性解的存在性[J].应用数学学报,1997,20(2):209-220. |
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| 作者姓名： | 项阳 |
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| 作者单位： | 清华大学应用数学系!北京，100084 |
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| 摘 要： | 本文研究了Ｒ＾Ｎ中的非线性退化椭圆型方程Ｆ（Ｄｕ，Ｄ＾２ｕ）＋ｕｓ＝ｆ的非负粘性解的存在性，其中ｓ〉０，Ｆ满足某些关于ｐ的条件，本文在下面的条件下证明了存在性；１．ｓ〉ｐ－１，ｆ在无穷远处不需要增长条件；２．０〈ｓ≤ｐ－１，ｆ在无穷远处具有某种增长条件。
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| 关 键 词： | 粘性解 存在性 非线性退化 椭圆型方程 |
EXISTENCE FOR VISCOSITY SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS IN RN |
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| XIANG YANG.EXISTENCE FOR VISCOSITY SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS IN RN[J].Acta Mathematicae Applicatae Sinica,1997,20(2):209-220. |
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| Authors: | XIANG YANG |
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| Abstract: | This paper is concerned with the existence for nonnegative viscosity solutions of the nonlinear degenerate elliptic equation F(Du, D2u) us = f in RN, where s > 0, F satisfies some conditions about p (p > 2). We prove the existence when s > p - 1, f without any growth condition at infinity or 0 < s < p - 1, f with some growth conditions at infinity. These extend the results about divergent equations in 1], 2] and 3] to the fully nonlinear degenerate case. |
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| Keywords: | Viscosity solution existence nonlinear degenerate |
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