The influence of domain geometry in boundary blow-up elliptic problems. (Q5960860)

This paper is devoted to the semilinear elliptic equation with explosion at the boundary NEWLINE\[NEWLINE\begin{gathered} -\Delta u+ u^p= 0\quad\text{in }\Omega,\\ u(x)\to +\infty\quad\text{as dist}(x,\partial\Omega)\to 0.\end{gathered}\tag{1}NEWLINE\]NEWLINE 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.