A second-order estimate for blow-up solutions of elliptic equations

✍ Scribed by Shuibo Huang; Qiaoyu Tian; Shengzhi Zhang; Jinhua Xi

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 246 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.11.037

✦ Synopsis

We investigate second-term asymptotic behavior of boundary blow-up solutions to the x) is a non-negative weight function. The nonlinearly f is regularly varying at infinity with index ρ > 1 (that is lim u→∞ f (ξ u)/f (u) = ξ ρ for every ξ > 0) and the mapping f (u)/u is increasing on (0, +∞). The main results show how the mean curvature of the boundary ∂Ω appears in the asymptotic expansion of the solution u(x). Our analysis relies on suitable upper and lower solutions and the Karamata regular variation theory.