Potential theoretic study for elliptic partial differential equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540174
• 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(研究院), 教授 (50294476)
• Co-Investigator(Kenkyū-buntansha): MIZUTA Yoshihiro 広島工業大学, 工学部, 教授 (00093815)
• Project Period (FY): 2012-04-01 – 2015-03-31
• 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 with variable exponents. As an application of the boundedness of the maximal operator, we establish a generalization of Sobolev's inequality and Trudinger's exponential inequality for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces with variable exponents.

Free Research Field

実解析