Potential theoretic study for elliptic partial differential equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04929
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hiroshima University
• Principal Investigator: SHIMOMURA TETSU 広島大学, 教育学研究科, 教授 (50294476)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: ソボレフ関数 / 楕円型偏微分方程式

Outline of Final Research Achievements

Variable exponent Lebesgue spaces and Sobolev spaces were introduced to discuss nonlinear partial differential equations with non-standard growth condition. These spaces have attracted more and more attention in connection with the study of elasticity and electrorheological fluids. In this research, we studied the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz-Morrey spaces and grand Musielak-Orlicz-Morrey spaces. As an application of the boundedness of the maximal operator, we establish a generalization of Sobolev's inequality, Trudinger's exponential inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces and grand Musielak-Orlicz-Morrey spaces.

Free Research Field

実解析