Nonlinear elliptical equations on the Sierpiński gasket
type: Item
instance of: scholarly article
title: Nonlinear elliptical equations on the Sierpiński gasket
zbMATH Open document ID: 0942.35070
author: Jiaxin Hu
author: Kenneth J. Falconer
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-07-25T00:00:00Z
review text: The authors investigate a question on the nontrivial solutions for the equation \(\Delta u + a(x)u=f(x,u)\) with zero Dirichlet conditions on the Sierpiński gasket. There are results both for a standard (in this theory) Laplacian and for a weak one. Some of the used general functional tools are: mountain pass theorem and saddle point theorem.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1417581
zbMATH Keywords: Sierpiński gasket
zbMATH Keywords: Laplacian operator
zbMATH Keywords: weak solution
zbMATH Keywords: mountain pass theorem
zbMATH Keywords: saddle point theorem
zbMATH Keywords: Sobolev-type inequality
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6617
OpenAlex ID: W2046133471
cites work: Dual variational methods in critical point theory and applications
cites work: Transition densities for Brownian motion on the Sierpinski carpet
cites work: Brownian Motion and Harmonic Analysis on Sierpinski Carpets
cites work: Q3995301
cites work: Techniques in fractal geometry
cites work: Semilinear PDEs on self-similar fractals
cites work: On a spectral analysis for the Sierpiński gasket.
cites work: Q5631509
cites work: Q4279837
cites work: Harmonic Calculus on P.C.F. Self-Similar Sets
cites work: Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
cites work: Harmonization and homogenization on fractals
cites work: Q4232748
cites work: Q4375665
cites work: Q5516356
cites work: Spectral asymptotics for variational fractals
cites work: Q3918776
cites work: Q3749777
cites work: Some properties of Laplacians on fractals
cites work: Splines on fractals
cites work: Q5620934
DOI: 10.1006/JMAA.1999.6617
description: scientific article; zbMATH DE number 1417581