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 \[ \begin{gathered} -\Delta u+ u^p= 0\quad\text{in }\Omega,\\ u(x)\to +\infty\quad\text{as dist}(x,\partial\Omega)\to 0.\end{gathered}\tag{1} \] 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.


35J65 Nonlinear boundary value problems for linear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35J60 Nonlinear elliptic equations
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