The critical Hardy inequality and its application to partial differential equations with logarithmic singularity

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17575
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Ehime University
• Principal Investigator: ioku norisuke 愛媛大学, 理工学研究科(理学系), 准教授 (50624607)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: スケール不変性 / 熱方程式 / Hardyの不等式 / 最良定数

Outline of Final Research Achievements

We clarified a scale invariance structure of the critical Hardy inequality. Namely, we proved that the higher order remainder term is automatically determined by the scale invariance property. Moreover, we investigated classification results of existence and nonexistence of the heat equation with general nonlinearity, and proved its threshold integrability of the initial data. In addition, if the nonlinear term is an exponential type, we obtained the classification of uniqueness and non uniqueness results.

Free Research Field

偏微分方程式論