The second order expansion of boundary blow-up solutions for infinity-Laplacian equations

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• 作者：Haitao Wan ^{wanhaitao200805@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Infinity Laplacian ; Viscosity solutions ; Boundary blow-up
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：436
• 期：1
• 页码：179-202
• 全文大小：456 K

文摘

In this paper, by using Karamata regular variation theory and a perturbed argument, we study the second order expansion of viscosity solutions to boundary blow-up elliptic problem Δ_∞u=b(x)f(u)${\mathrm{\Delta }}_{\infty }u=b(x)f(u)$, x∈Ω$x\in \mathrm{\Omega }$, a20c2049d9f16c6e6e" title="Click to view the MathML source">u|_∂Ω=+∞${u|}_{\partial \mathrm{\Omega }}=+\infty$, where Ω is a bounded domain with C²$C^2$-boundary in R^N${\mathbb{R}}^N$, $b\in \mathrm{C}(\overline{\mathrm{\Omega }})$ is non-negative and non-trivial in Ω, f∈C¹([0,∞))$f\in C^1([0,\infty ))$ is a normalized regularly varying function at infinity with index 41a2c5241e480d160b1557a38" title="Click to view the MathML source">γ>3$\gamma >3$.