Global and asymptotic analysis of critical variational problems with mass/energy concentration phenomena

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340038
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Osaka City University
• Principal Investigator: TAKAHASHI Futoshi 大阪市立大学, 大学院理学研究科, 教授 (10374901)
• Co-Investigator(Kenkyū-buntansha): KATO Shin 大阪市立大学, 大学院理学研究科, 准教授 (10243354) ; NISHIO Masaharu 大阪市立大学, 大学院理学研究科, 准教授 (90228156) ; ISHIWATA Michinori 大阪大学, 大学院基礎工学研究科, 准教授 (30350458) ; SATO Yohei 埼玉大学, 理工学研究科, 准教授 (00465387) ; WATANABE Tatsuya 京都産業大学, 理学研究科, 准教授 (60549749)
• Co-Investigator(Renkei-kenkyūsha): OHNITA Yoshihiro 大阪市立大学, 大学院理学研究科, 教授 (90183764) ; SUZUKI Takashi 大阪大学, 大学院基礎工学研究科, 教授 (40114516)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 臨界型変分問題 / 爆発解析 / 多重バブル解 / 質量集中現象 / コンパクト性の損失

Outline of Final Research Achievements

In this research program, we study the qualitative and quantitative properties of multi-bubble solutions to the variational problems of critical type. The main 4 subjects of research are (1) Structure of spaces of multi-bubble solutions and its relation to the domain geometry (2) Study of the spectral properties of multi-bubble solutions (3) Qualitative properties of multi-bubble solutions induced by the concentration and blow-up (4) Characterization of the set of blow-up points of multi-bubble solutions. Total 35 research papers are published in the international journals and 17 research reports at the Mathematical Society of Japan are presented.

Free Research Field

変分法・非線形偏微分方程式論