Analysis on the behavior and the singularity of solutions to fully nonlinear elliptic and parabolic partial differential equations
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 |
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
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 / 解析学 |
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.
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Report
(5 results)
Research Products
(17 results)