2013 Fiscal Year Final Research Report
Towards de Giorgi-Nash-Moser theory on non-linear non-local partial differential equations.
| Project/Area Number |
24654033
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
ISHIGE Kazuhiro 東北大学, 大学院理学研究科, 教授 (90272020)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Keywords | 非局所偏微分方程式 / 確率論 / 解析学 / 飛躍型確率過程 / 国際研究者交流 / フィンランド：韓国：ポーランド：アメリカ |
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| Research Abstract |
We investigated recently developed methods on the de Giorgi-Nash-Moser theory and a priori estimates of caloric functions for non-local operators and jump-type stochastic processes. We gave some sufficient conditions for the boundary Harnack inequalities to hold for jump-type processes (non-local operators) on general metric measure spaces, and applied the results to various concrete examples. We also worked on heat kernel estimates for fractional time derivative heat equations.
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