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Fractal Reinforcement of Elastic Membranes

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Abstract

We describe a homogenization model of an elastic membrane reinforced by the inclusion of a fractal string. We follow a variational approach consisting in proving the convergence of certain energy functionals. This leads to the spectral convergence of a sequence of weighted second-order elliptic partial differential operators to a singular elliptic operator with a fractal term.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, 01609-2280, USA

    Umberto Mosco

  2. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università degli Studi di Roma “La Sapienza”, Via A. Scarpa 16, 00161, Rome, Italy

    Maria Agostina Vivaldi

Authors
  1. Umberto Mosco
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  2. Maria Agostina Vivaldi
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Correspondence to Umberto Mosco.

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Communicated by D. Kinderlehrer

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Mosco, U., Vivaldi, M.A. Fractal Reinforcement of Elastic Membranes. Arch Rational Mech Anal 194, 49–74 (2009). https://doi.org/10.1007/s00205-008-0145-1

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  • DOI: https://doi.org/10.1007/s00205-008-0145-1

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