BIMSA >
BIMSA Lecture
BIMSA Lecture
Pointwise estimates and existence classification results for fully nonlinear elliptic equations with nonzero Dirichlet conditions
Pointwise estimates and existence classification results for fully nonlinear elliptic equations with nonzero Dirichlet conditions
Organizer
Speaker
Mengni Li
Time
Thursday, April 2, 2026 2:00 PM - 3:00 PM
Venue
Shuangqing-B725
Online
Zoom 242 742 6089
(BIMSA)
Abstract
This talk mainly concerns two aspects of fully nonlinear elliptic equations with nonzero Dirichlet conditions. In the first aspect, we develop pointwise boundary upper and lower bound estimates for convex solutions based on the subsolution and supersolution method. The global Hölder regularity can be derived as a direct consequence of these pointwise boundary estimates. In the second aspect, we provide a complete classification on the existence and nonexistence results of viscosity solutions to the general Dirichlet problem for a class of eigenvalue type equations. Moreover, when viscosity solutions exist, we derive a series of global estimates based on the distance function.