Variational approach to elliptic partial differential equations associated with critical functional inequalities

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K21056
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis; Mathematical analysis
• Research Institution: Kanazawa University
• Principal Investigator: Wadade Hidemitsu 金沢大学, 機械工学系, 准教授 (00466525)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 臨界関数不等式 / 楕円型不等式 / 変分解析

Outline of Final Research Achievements

(1)One of applicant's main research is (*) to establish several functional inequalities concerning Sobolev's embedding theorem, and (**) to investigate the solutions of Euler-Lagrange equations (elliptic partial differential equations) associated with functional inequalities. (2)Another one is to re-consider the relations between themes (*) and (**), and to give a systematic approach for those themes (*) and (**). As a result, applicant succeeded in publishing several academic papers related on the themes (1) and (2).

Free Research Field

実解析

Academic Significance and Societal Importance of the Research Achievements

応募者の主な研究テーマはソボレフ空間上の種々の臨界不等式、または同不等式からEuler-Lagrange方程式を介して得られる楕円型方程式の可解性を論じることである。一般に、ソボレフ空間は関数空間、関数解析および物理的応用という観点における基礎的な空間であり、同空間の諸性質の精緻な解析は、数学的および物理的な応用という意味において多くの効果が期待される。