A study of the structure of the solutions of nonlinear elliptic equations in spaces of constant curvature

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04973
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical 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: Kohtaro Watanabe 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), 電気情報学群, 教授 (30546057)
• Co-Investigator(Kenkyū-buntansha): 山岸 弘幸 東京都立産業技術高等専門学校, ものづくり工学科, 准教授 (10448053)
• Co-Investigator(Renkei-kenkyūsha): KAMETAKA Yoshinori 大阪大学, 名誉教授 (00047218) ; SHIOJI Naoki 横浜国立大学, 大学院工学研究院, 教授 (50215943)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 一般化Pohozaev関数 / 正値球対称解 / 定曲率空間 / p-ラプラス作用素

Outline of Final Research Achievements

According to the initial plan, uniqueness of the positive radial solution of nonlinear elliptic equations in the space of constant curvature thorough generalized Pohozaev identity and its non-degeneracy, properties of the solutions of the Euler-Lagrange equations including p-Laplace operator in the space of constant curvature and detection of best constant of discrete Sobolev inequality were studied. Results of these studies were published in four papers. Although the study of p-Laplace operator in the space of constant curvature could not show significant progress. The result of this study is not published at present.

Free Research Field

函数方程式論