Research on the variational problems for the functionals with non-standard growth

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400177
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: Tachikawa Atsushi 東京理科大学, 理工学部数学科, 教授 (50188257)
• Co-Investigator(Renkei-kenkyūsha): NAGASAWA Takeyuki 埼玉大学, 理学研究科, 教授 (70202223)
• Research Collaborator: Maria Alessandra Ragusa Università degli Studi di Catania, Dipartimento di Matematica e Informatica, Professore Associato ; Antonia Passarelli di Napoli Università degli Studi di Napoli “Federico II", Dipartimento di Matematica e Applicazioni “R. Caccioppoli", Professore Associato ; Flavia Giannetti Università degli Studi di Napoli “Federico II", Dipartimento di Matematica e Applicazioni “R. Caccioppoli", Ricercatore
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 関数方程式論 / 変分問題 / non-standard growth

Outline of Final Research Achievements

The problem of finding critical points of a given "quantity" (functional) is called a variational problem. When we try to solve a variational problem, we often employ the method consisting of the following 2-steps: first, we find a "weakly differentiable solution" =weak solution, and, in the second step, we show that the weak solution is differentiable sufficiently for the problem under consideration. This second step is called as "regularity problem". In this research, we treated the regularity problems for the functionals of non-standard growth, especially, for so-called p(x)-growth functionals, and have gotten some new results.

Free Research Field

偏微分方程式論