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Boundary behavior of large solutions to semilinear elliptic equations with weights

This talk is concerned with boundary blow-up elliptic problems \ $\triangle u =b(x)f(u)$, $x\in \xO, \ \ u|_{\partial\Omega}=+\infty,$ where $\Omega$ is a bounded domain with smooth boundary in $\mathbb R^N$, and $b \in C^\alpha_{\rm loc}({\xO})$ for some $\alpha\in (0, 1)$ which is nonnegative nontrivial in $\Omega$, but may be vanishing or appropriate singular (including critical singular) on $\partial \Omega$. Under a new structure condition on $f$ near infinity, we study the exact boundary behavior of such solutions.