2010 Fiscal Year Final Research Report
Viscosity solution theory for fully nonlinear equations and its applications
| Project/Area Number |
20340026
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Saitama University |
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Principal Investigator |
KOIKE Shigeaki 埼玉大学, 大学院・理工学研究科, 教授 (90205295)
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| Co-Investigator(Kenkyū-buntansha) |
ISHII Hitoshi 早稲田大学, 教育総合科学学術院, 教授 (70102887)
MIKAMI Toshio 広島大学, 大学院・工学研究科, 教授 (70229657)
ISHII Katsuyuki 神戸大学, 大学院・海事科学研究科, 准教授 (40232227)
NAGAI Hideo 大阪大学, 大学院・基礎工学研究科, 教授 (70110848)
MORIMOTO Hiroaki 愛媛大学, 大学院・理工学研究科, 教授 (80166438)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 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 |
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| Research Abstract |
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.
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