Weekly Activities

Elliptic solutions to nonsymmetric Monge-Amp\`{e}re type equations I. The $d$-concavity and the comparison principle
Speaker: Thai Thi Kim Chung

Time: 9h30, Tuesday, December 5, 2017
Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: We consider the Dirichlet problem for nonsymmetric Monge-Amp\`{e}re type equations, in which a skew-symmetric matrix is introduced. We establish uniform with respect to a class of skew-symmetric matrices bounds for $\delta$-elliptic $C^{2, \alpha}(\overline{\Omega})$-solutions to the Dirichlet problem. Then we prove the classical solvability of the Dirichlet problem, provided those skew-symmetric matrices are sufficiently small in some sence.