We study spectral asymptotic properties of conductive layered-thin-fibers of invasive fractal nature. The problem is formulated as a boundary value problem for singular elliptic operators with potentials in a quasi-filling geometry for the fibers. The methods are those of variational singular homogenization and M-convergence. We prove that the spectral measures of the differential problems converge to the spectral measure of a non-trivial self-adjoint operator with fractal terms.
Layered fractal fibers and potentials / U., Mosco; Vivaldi, Maria Agostina. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 103 n°5:(2015), pp. 1198-1227. [10.1016/j.matpur.2014.10.010]
Layered fractal fibers and potentials
VIVALDI, Maria Agostina
2015
Abstract
We study spectral asymptotic properties of conductive layered-thin-fibers of invasive fractal nature. The problem is formulated as a boundary value problem for singular elliptic operators with potentials in a quasi-filling geometry for the fibers. The methods are those of variational singular homogenization and M-convergence. We prove that the spectral measures of the differential problems converge to the spectral measure of a non-trivial self-adjoint operator with fractal terms.| File | Dimensione | Formato | |
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