Higher Order Estimates for Boundary Blow-Up Solutions of Elliptic Equations with Gradient Term
Received:March 24, 2020  Revised:October 24, 2020
Key Word: second order estimates   third order estimates   semilinear elliptic equations
Fund ProjectL:Supported by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos.LY20A010010; LY20A010011), the National Natural Science Foundation of China (Grant No.11971251) and K. C. Wong Magna Fund in Ningbo University.
 Author Name Affiliation Yajie ZHANG Department of Mathematics, Ningbo University, Zhejiang 315000, P. R. China Feiyao MAO Department of Mathematics, Ningbo University, Zhejiang 315000, P. R. China Weifeng WO Department of Mathematics, Ningbo University, Zhejiang 315000, P. R. China
Hits: 83
In this paper, the higher order asymptotic behaviors of boundary blow-up solutions to the equation $\Delta\,u={u}^{p}\pm |\nabla u|^{q}$ in bounded smooth domain $\Omega \subset {R}^{N}$ are systematically investigated for $p$ and $q$. The second and third order boundary behaviours of the equation are derived. The results show the role of the mean curvature of the boundary $\partial \Omega$ and its gradient in the high order asymptotic expansions of the solutions.