Refinement of analytic inequalities with geometric approach

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540199
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群)
• Principal Investigator: WATANABE Kohtaro 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, その他部局等, 教授 (30546057)
• Co-Investigator(Kenkyū-buntansha): KAMETAKA Yoshinori 大阪大学, 名誉教授 (00047218) ; SHIOJI Naoki 横浜国立大学, 工学研究院, 教授 (50215943)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 非線形微分方程式 / 球対称性 / 解の一意性

Outline of Final Research Achievements

According to the plan of this study, we have proceeded the following two objects: the extension of Gidas-Ni-Nirenberg's theory by the geometric approach, refinements of Lyapunov-type inequalities and their applications to half-liear equations which include p-Laplacian.
In the former, we have studied (1) Henon equation, especially the construction problem of non-radially symmetric solutions (m-mode solutions) and their degeneracy to radially symmetric solutions. (2) Brezis-Nirenberg problem on n-dimensional sphere and the uniqueness of the solution. These results are published in three papers.
In the latter, we have studied Sobolev inequalities which are necessary for the refinements of Lyapunov-type inequalities. These results are published in 13 papers.

Free Research Field

函数方程式論