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Zbl 1142.35431
del Pino, Manuel; Letelier, René
The influence of domain geometry in boundary blow-up elliptic problems.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 48, No. 6, A, 897-904 (2002). ISSN 0362-546X

This paper is devoted to the semilinear elliptic equation with explosion at the boundary $$\gathered -\Delta u+ u^p= 0\quad\text{in }\Omega,\\ u(x)\to +\infty\quad\text{as dist}(x,\partial\Omega)\to 0.\endgathered\tag1$$ 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.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
35B40 Asymptotic behavior of solutions of PDE
35J60 Nonlinear elliptic equations

Keywords: domain geometry; explosion rate; elliptic problem

Cited in: Zbl 1129.35312

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