Title:  Interior C^{1,1} regularity of solutions to degenerate Monge-Ampere type equations

Reporter:  JIANG Feida

Date:  2019.11.18    11:00-12:00

Place:  School of Science  Room 212

Abstract:  In this talk, we present the interior C^{1,1} regularity of viscosity solutions for a degenerate Monge-Ampere type equation when the (n-1)-th root of the right hand side function is C^{1,1} smooth. We will talk about the cases when the matrix function satisfies the A3 condition and A3w+ condition respectively. In the former case, we construct a suitable auxiliary function to obtain uniform a priori estimates directly. In the latter case, the main argument is to establish the Pogorelov type estimates, which are interesting independently. The degenerate Monge-Ampere equation in the standard form will also be discussed.