開催日時
2019/11/08 金 15:30 - 17:30
場所
3号館251号室
講演者
舘山 翔太
講演者所属
早稲田大学理工学術院
概要
We discuss fully nonlinear second order uniformly parabolic equations including Isaacs parabolic equations. Isaacs equations arise in the theory of stochastic differential games. In 2014, N.V. Krylov proved the existence of $L^p$-viscosity solutions of boundary value problems for equations with VMO (vanishing mean oscillation) "coefficients" when $p>n+2$. Furthermore, the solutions were in the parabolic Hölder space $C^{1+\alpha, \frac{1+\alpha}{2}}$ for $\alpha\in(0, 1)$. Our purpose is to show interior Hölder estimates on the spatial gradients of $L^p$-viscosity solutions of fully nonlinear parabolic equations under the same conditions as in Krylov's result.