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Elliptic Problems on the Sierpinski Gasket

In: Topics in Mathematical Analysis and Applications

Author

Listed:
  • Brigitte E. Breckner

    (Babeş-Bolyai University)

  • Csaba Varga

    (Babeş-Bolyai University)

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.

Suggested Citation

  • Brigitte E. Breckner & Csaba Varga, 2014. "Elliptic Problems on the Sierpinski Gasket," Springer Optimization and Its Applications, in: Themistocles M. Rassias & László Tóth (ed.), Topics in Mathematical Analysis and Applications, edition 127, pages 119-173, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-06554-0_6
    DOI: 10.1007/978-3-319-06554-0_6
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