Explore of undiscovered variational principles in function spaces in real analysis

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610030
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical 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(Renkei-kenkyūsha): IOKU Norisuke 愛媛大学, 大学院理工学研究科, 准教授 (50624607)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 函数不等式 / 変分原理 / Hardy 不等式 / Trudinger-Moser 不等式

Outline of Final Research Achievements

The aim of this research is to understand the variational structures of several functional inequalities, such as Trudinger-Moser, Sobolev, and Hardy type, which are established newly in various functional spaces such as Lorentz, and Orlicz, and to find new applications to PDE theories.More precise research subjects are the following:(1) Sobolev-Orlicz approach to elliptic systems with the indefinite variational structures, (2) Study of the Trudinger-Moser type inequalities and their variational structures (3) Hardy type inequalities of the scale invariant form and its application to the stability theory of　solutions.

Free Research Field

変分法・偏微分方程式論