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TWO NONTRIVIAL WEAK SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPIŃSKI GASKET

Part of: Elliptic equations and systems Other generalizations Classical measure theory

Published online by Cambridge University Press:  12 December 2011

DENISA STANCU-DUMITRU
DENISA STANCU-DUMITRU*
Affiliation:
Department of Mathematics, University of Craiova, 200585 Craiova, Romania (email: [email protected])
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Abstract

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We study a Dirichlet problem involving the weak Laplacian on the Sierpiński gasket, and we prove the existence of at least two distinct nontrivial weak solutions using Ekeland’s Variational Principle and standard tools in critical point theory combined with corresponding variational techniques.

Keywords

Sierpiński gasketweak LaplacianDirichlet formweak solutionEkeland’s variational principle

MSC classification

Secondary: 28A80: Fractals 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 31C25: Dirichlet spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 395 - 414
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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