A boundary expansion of solutions to nonlinear singular elliptic equations

Jian, Huaiyu; Lu, Jian; Wang, Xu-Jia

Cultural advice

The Australian National University acknowledges, celebrates and pays our respects to the Ngunnawal and Ngambri people of the Canberra region and to all First Nations Australians on whose traditional lands we meet and work, and whose cultures are among the oldest continuing cultures in human history.

Aboriginal and Torres Strait Islander peoples are advised that ANU Library collections may include images, names, voices, and other representations of deceased persons.

Material in the collection may contain terms, language or views that reflect the period in which the item was created and may be considered inappropriate today.

A boundary expansion of solutions to nonlinear singular elliptic equations

Date

2021

Authors

Jian, Huaiyu

Lu, Jian

Wang, Xu-Jia

Publisher

Zhongguo Kexue Zazhishe/Science in China Press

Abstract

In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary. This expansion formula shows the singularity profile of solutions at the boundary. We deal with both linear and nonlinear elliptic equations, including fully nonlinear elliptic equations and equations of Monge-Ampère type.