A boundary expansion of solutions to nonlinear singular elliptic equations

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. Show more