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The influence of domain geometry in boundary blow-up elliptic problems. (English) Zbl 1142.35431

This paper is devoted to the semilinear elliptic equation with explosion at the boundary

$\begin{array}{c}-{\Delta }u+{u}^{p}=0\phantom{\rule{1.em}{0ex}}\text{in}\phantom{\rule{4.pt}{0ex}}{\Omega },\\ u\left(x\right)\to +\infty \phantom{\rule{1.em}{0ex}}\text{as}\phantom{\rule{4.pt}{0ex}}\text{dist}\left(x,\partial {\Omega }\right)\to 0·\end{array}\phantom{\rule{2.em}{0ex}}\left(1\right)$

More precisely, the authors address the following question: how does local geometry of the boundary influence the blow-up behaviour of a solution to (1). The authors “show” that the “more curved” or “sharper” towards the exterior a domain is around a given point of its boundary, the higher the explosion rate at that point is.

##### MSC:
 35J65 Nonlinear boundary value problems for linear elliptic equations 35B40 Asymptotic behavior of solutions of PDE 35J60 Nonlinear elliptic equations
##### Keywords:
domain geometry; explosion rate; elliptic problem