Free boundary problems of PDEs with degeneracy-singularity

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540218
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Shibaura Institute of Technology
• Principal Investigator: TAKEUCHI Shingo 芝浦工業大学, システム理工学部, 教授 (00333021)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: p-Laplacian / 一般化ヤコビ楕円関数 / 一般化三角関数

Outline of Final Research Achievements

Through this research project, the relation between the eigenfunctions of p-Laplacian and fundamental concepts of number theory, such as elliptic integral, elliptic function, hypergeometric function, arithmetic-geometric mean, etc., has come to be seen. We gave generalization of Jacobi elliptic function and the complete elliptic integral by generalized trigonometric functions, and as their application we presented Gauss-Legendre's type algorithm on the constant pi and generalization and expressions of solutions for classical differential equations. Regarding these series of results, we have received certain evaluations from P. Lindqvist, R. Manasevich, and M. Vuorinen, who are famous for research on p-Laplacian including generalized trigonometric functions, We believe that knowledge leading to cross-cutting research has been obtained.

Free Research Field

非線形偏微分方程式