Elliptic Problems on the Sierpinski Gasket

Brigitte E. Breckner () and Csaba Varga ()
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Brigitte E. Breckner: Babeş-Bolyai University
Csaba Varga: Babeş-Bolyai University

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 119-173 from Springer

Abstract: Abstract There are treated nonlinear elliptic problems defined on the Sierpinski gasket, a highly non-smooth fractal set. Even if the structure of this fractal differs considerably from that of (open) domains of Euclidean spaces, this note emphasizes that PDEs defined on it may be studied (as in the Euclidean case) by means of certain variational methods. Using such methods, and appropriate abstract multiplicity theorems, there are proved several results concerning the existence of multiple (weak) solutions of Dirichlet problems defined on the Sierpinski gasket.

Keywords: Sierpinski gasket; Weak Laplacian; Dirichlet problem on the Sierpinski gasket; Weak solution; Critical point (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_6

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DOI: 10.1007/978-3-319-06554-0_6

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