Semilinear PDEs on self-similar fractals
type: Item
instance of: scholarly article
title: Semilinear PDEs on self-similar fractals
zbMATH Open document ID: 0940.35080
published in: Communications in Mathematical Physics
publication date: 2000-06-07T00:00:00Z
review text: The author considers a Laplacian on self-similar fractal domains defined in terms of a suitable self-similar Dirichlet form, see \textit{U. Mosco} [AMS/IP Stud. Adv. Math. 8, 117-155 (1998; Zbl 0914.31007)]. It is shown that the semilinear equations such as \(\Delta u +u^p=0\) with zero Dirichlet boundary conditions have nontrivial nonnegative solution for any \(p>1\) if \(0<\nu\leq 2\), and for \(1<p<(\nu+2)/(\nu-2)\) if \(\nu>2\), where \(\nu\) is the intrinsic dimension of the fractal domain.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 35J99
zbMATH DE Number: 1382933
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: fractals
zbMATH Keywords: nontrivial solutions
zbMATH Keywords: critical exponent
author: Kenneth J. Falconer
reviewed by: E. A. Kalita
MaRDI profile type: Publication
full work available at URL: s002200050703
OpenAlex ID: W2044161930
DOI: 10.1007/S002200050703
description: scientific article; zbMATH DE number 1382933