Viscosity solution theory for fully nonlinear equations and its applications

全非线性方程粘度解理论及其应用

• 批准号: 20340026
• 负责人: KOIKE Shigeaki
• 金额: $ 9.48万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340026/
• 关键词: 粘性解; 楕円性; 完全非線形方程式; 最大値原理; ハルナック不等式; 比較原理; 弱ハルナック不等式; プラグメン・リンデレフ定理; 局所最大値原理; 確率最適制御; Lp粘性解; ABP最大値原理; Phragmen-Lindelov定理; Pucci方程式

The basic theory for viscosity solutions of fully nonlinear second order elliptic partial differential equations is studied. In case when uniformly elliptic equations contain unbounded coefficients to the first derivatives, it is proved that the weak Harnack inequality holds for Lp-viscosity solutions. As applications, it turns out that qualitative properties such as the strong maximum principle, the maximum principle for unbounded domains, the Phragmen-Lindelov theorem etc. are shown.In case when degenerate elliptic equations contain the first derivative terms with supearlinear growth, by setting appropriate function spaces, to which viscosity solutions belong, the comparison principle for them is proved.

研究了完全非线性二阶椭圆型偏微分方程粘性解的基本理论。当一致椭圆型方程的一阶导数系数无界时，证明了弱Harnack不等式对Lp粘性解成立.作为应用，给出了强极大值原理、无界区域的极大值原理、Phragmen-Lindelov定理等定性性质，并在退化椭圆型方程含有超线性增长的一阶导数项的情况下，通过设置适当的函数空间，证明了粘性解的比较原理.

项目成果

Weak Harnack inequality for fully nonlinear PDEs with unbounded ingredients

具有无界成分的完全非线性偏微分方程的弱 Harnack 不等式

• 发表时间: 2010
• 作者: Yoshio Miyahara;K. Matsuzaki;徳重典英;小池茂昭
• 通讯作者: 小池茂昭

Optimal consumption in a growth model with the Cobb-Doualas oroduction function

具有柯布-杜阿拉产出函数的增长模型中的最优消耗

• 发表时间: 2008
• 期刊: SIAM Journal in Control and Optimization 47巻
• 作者: T. Kawai;T. Koike and Y. Takei;H. Nagai;H.Maehara;K. Matsuzaki;H. Morimoto and X. Y. Zhou
• 通讯作者: H. Morimoto and X. Y. Zhou

On viscosity solutions of fully nonlinear elliptic PDE with measurable and unbounded ingredients

具有可测无界成分的全非线性椭圆偏微分方程的粘度解

• 发表时间: 2011
• 作者: A.Kohatsu-Higa;S.Ortiz;小池茂昭
• 通讯作者: 小池茂昭

On the weak Hamack inequality for fully nonlinear PDEs with unbounded ingredients

关于具有无界成分的完全非线性偏微分方程的弱 Hamack 不等式

• 发表时间: 2010
• 作者: Q.Pan;R.Nishii;T.Nakagawa;T.Nakamoto;徳重典英;小池茂昭
• 通讯作者: 小池茂昭

Weak Harnack inequality for Lp-viscosity solutions of fully nonlinear elliptic PDEs with unbounded ingredients

具有无界成分的完全非线性椭圆偏微分方程的 Lp 粘度解的弱 Harnack 不等式

• 发表时间: 2009
• 作者: Masanori Kato;Akira Endo;Shingo Katsumoto and Yasuhiro Iye;上山大信;S.Koike
• 通讯作者: S.Koike