On the asymptotics near the piecewise smooth boundary of singular solutions of semilinear elliptic equations
type: Item
instance of: scholarly article
title: On the asymptotics near the piecewise smooth boundary of singular solutions of semilinear elliptic equations
zbMATH Open document ID: 0836.35027
DOI: 10.1007/BF02110557
published in: Mathematical Notes
publication date: 1996-04-29T00:00:00Z
review text: We consider the problem (1) \(Lu = \sum^N_{i,j = 1} a_{ij} (x) u_{x_ix_j} + \sum^N_{i = 1} a_i (x) u_{x_i} - a(x) u = p(x) u^k\), \(u > 0\), \(x \in G\), \(\lim_{x \to \Gamma} u(x) = + \infty\), where \(G\) is a bounded domain whose boundary \(\Gamma\) is a piecewise smooth surface containing singularities of two types, conic points and edges; \(L\) is a uniformly elliptic operator in \(\overline G\); the coefficients of Eq. (1) belong to \(C^2 (\overline G)\); \(p(x) > 0\), \(a(x) \geq 0\), \(k > 1\), \(N \geq 2\). We obtain the asymptotics of the solution in the neighborhood of conic points and of edges of the boundary.
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 830688
zbMATH Keywords: estimates for the second term of the asymptotics
zbMATH Keywords: conic points
zbMATH Keywords: edges
author: V. A. Kondrat'ev
author: Valery A. Nikishkin
MaRDI profile type: Publication
cites work: Q3349992
cites work: `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
cites work: Semilinear elliptic equations with uniform blow-up on the boundary
cites work: Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains
full work available at URL: https://doi.org/10.1007/bf02110557
OpenAlex ID: W2036481046
description: scientific article; zbMATH DE number 830688