Boundary-blow-up problems in a fractal domain
type: Item
instance of: scholarly article
title: Boundary-blow-up problems in a fractal domain
zbMATH Open document ID: 0853.35042
DOI: 10.4171/ZAA/708
author: Jerk Matero
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1997-01-05T00:00:00Z
review text: Boundary blow up problems for the problem \(\Delta u(x)= f(u(x))\) are considered in a bounded domain \(\Omega\subset \mathbb{R}^n\), \(n\geq 2\), which satisfies a uniform interior and exterior cone condition, and with \(f(t)= e^t\) or \(f(t)= t^p\) where \(p\in (1, +\infty)\). The author gives uniform a priori lower and upper bounds for the growth of the solutions and their gradients. A maximum principle is used to show the existence and the uniqueness of a solution. As an application, the problem in a two-dimensional domain whose boundary is the von Koch snowflake curve are presented.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 889005
zbMATH Keywords: fractal boundary
zbMATH Keywords: semilinear elliptic equation
reviewed by: Ding Hua
MaRDI profile type: Publication
cites work: On the Dirichlet problem for quasi-linear elliptic differential equations of the second order
cites work: Q4312129
cites work: On positive solutions of Emden equations in cone-like domains
cites work: On the Existence and Nonexistence of Global Solutions of Reaction-Diffusion Equations in Sectorial Domains
cites work: Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary
cites work: Q5839013
cites work: Elliptic Partial Differential Equations of Second Order
cites work: On solutions of δu=f(u)
cites work: On a Singular Nonlinear Elliptic Boundary-Value Problem
cites work: Q3141808
cites work: On the inequality \(\Delta u \geqq f (u)\)
description: scientific article; zbMATH DE number 889005