Analysis on the behavior and the singularity of solutions to fully nonlinear elliptic and parabolic partial differential equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400169
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Hiroshima University
• Principal Investigator: Kazuhiro Takimoto 広島大学, 理学研究科, 准教授 (00363044)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 完全非線形偏微分方程式 / 境界値問題 / 粘性解 / 解の存在と一意性 / 関数方程式

Outline of Final Research Achievements

We study the solvability of the boundary value problem, and the behavior and the singularity of solutions for fully nonlinear elliptic and parabolic partial differential equations. We also aim for the investigation of nonlinear phenomena. New results are obtained on the uniqueness of solutions to the so-called k-curvature equation, which is a fully nonlinear partial differential equation having geometric structure. Also, we obtain Bernstein type theorems for the generalized parabolic k-Hessian equation.

Free Research Field

非線形偏微分方程式論