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

MSC:

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