Asymptotic estimates of large solutions to the infinity Laplacian equations. (English) Zbl 1537.35078
Summary: The article is intend to study the asymptotic behavior of the large solutions near the boundary to the following infinity Laplace equation \(\triangle_{\infty}^h u =b(x)f(u)\), \(x\in \Omega\), \(u|_{\partial\Omega}=+\infty\), where \(\triangle_{\infty}^h u:= |Du|^{h-3}\langle D^2 uDu, Du\rangle\) for all \(h>1\), \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb{R}^N\), \(b \in C(\bar{\Omega})\) which is positive in \(\Omega\), and \(f\in C^1 (0,\infty)\) is positive increasing. The main feature of this paper is that the nonlinearity \(f\) is regularly varying at infinity with the critical index \(h\).
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35J60 | Nonlinear elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
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