2012 Fiscal Year Final Research Report
Free boundary problem with quasilinear elliptic equations
| Project/Area Number |
22540229
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Naruto University of Education |
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Principal Investigator |
NARUKAWA Kimiaki 鳴門教育大学, 大学院・学校教育研究科, 教授 (60116639)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUOKA Takashi 鳴門教育大学, 大学院・学校教育研究科, 教授 (50127297)
ITO Masayuki 徳島大学, ソシオ・アーツ・サイエンス研究部, 教授 (70136034)
FUKAGAI Nobuyoshi 徳島大学, ソシオテクノサイエンス研究部, 准教授 (90175563)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 変分法 / 準線形楕円型方程式 / 自由境界問題 / 臨界指数 / ディリクレ境界値問題 / 非線形ノイマン問題 |
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| Research Abstract |
We have investigated free boundary problems with quasilinear elliptic equations having nonhomogeneous principal parts, which appear oftenin the field of nonlinear elasticity, and non-Newtonian fluid etc. Especially the properties of positive solutions for Dirichlet and nonlinear Neumann problems for the equations with critical nonlinear terms and indefinite coefficients have been studied. These results are necessary to investigate the free boundary problem with quasilinear elliptic equations. Using these results, we challenged the variational problems appearing free boundaries.
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