偏微分方程研讨班:On concavity and subsolutions for fully nonlinear elliptic equations

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Professor Bo Guan (Ohio State University)   

题  目：On concavity and subsolutions for fully nonlinear elliptic equations

时  间：2023.12.04（星期一）上午10:00-11:00

地  点：思源楼S813

摘 要：Both subsolutions and concavity play important roles in a priori estimates and classical solvability of fully nonlinear elliptic equations. In this talk we explore the possibility to weaken the concavity condition. We shall also discuss generalized notions of subsolution introduced by Szekelyhidi and myself, respectively, to treat equations on closed manifolds, and clarify their relations. More precisely, we show that these weak notions of subsolutions are equivalent for equations defined on convex cones of type 1 in the sense defined by Caffarelli, Nirenberg and Spruck.