Chuaqui, M.; Cortazar, C.; Elgueta, M.; Garcia-Melian, J. Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights. (English) Zbl 1174.35386 Commun. Pure Appl. Anal. 3, No. 4, 653-662 (2004). In this paper the authors study the problems corresponding of power and exponential type, that is \[ \begin{cases} \Delta u=a(x)u^m\quad & \text{in }\Omega\\ u=+\infty & \text{on }\partial\Omega\end{cases}\tag{1} \] and \[ \begin{cases} \Delta v=a(x)e^v\quad & \text{in }\Omega\\ v=+\infty & \text{on }\partial\Omega,\end{cases}\tag{2} \] where the weight function \(a(x)\) is assumed to be Hölder continuous, growing like a negative power of \(d(x)=\text{dist}(x,\partial\Omega)\) near \(\partial\Omega\). The authors prove existence and nonexistence results, uniqueness and asymptotic estimates near the boundary for both the solutions and their normal derivatives. Reviewer: Messoud A. Efendiev (Berlin) Cited in 48 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B45 A priori estimates in context of PDEs Keywords:singular weights; nonexistence result; estimates near the boundary PDFBibTeX XMLCite \textit{M. Chuaqui} et al., Commun. Pure Appl. Anal. 3, No. 4, 653--662 (2004; Zbl 1174.35386) Full Text: DOI