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Tuesday Seminar of Analysis
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi |
2022/11/29
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
TAKIMOTO Kazuhiro (Hiroshima University)
Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)
https://forms.gle/93YQ9C6DGYt5Vjuf7
TAKIMOTO Kazuhiro (Hiroshima University)
Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)
[ Abstract ]
In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.
[ Reference URL ]In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.
https://forms.gle/93YQ9C6DGYt5Vjuf7
