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Pointwise estimates and existence classification results for fully nonlinear elliptic equations with nonzero Dirichlet conditions

组织者

傅二娟

演讲者

李梦妮

时间

2026年04月02日 14:00 至 15:00

地点

Shuangqing-B725

线上

Zoom 242 742 6089 (BIMSA)

摘要

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.