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.
Fractal Reinforcement of Elastic Membranes / Umberto, Mosco; Vivaldi, Maria Agostina. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 194:1(2009), pp. 49-74. [10.1007/s00205-008-0145-1]
Fractal Reinforcement of Elastic Membranes
VIVALDI, Maria Agostina
2009
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.File allegati a questo prodotto
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