| Higher Order Estimates for Boundary Blow-Up Solutions of Elliptic Equations with Gradient Term |
| Received:March 24, 2020 Revised:October 24, 2020 |
| Key Words:
second order estimates third order estimates semilinear elliptic equations
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| Fund Project: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. |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2021.02.005 |
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