We construct a sequence of quadratic weighted energy forms in an open domain of the plane, which M-converges to the an energy form with a singular fractal term. The weights belong to the A_2-Muckenoupt class and have point-wise singularities. The result implies the spectral convergence of a sequence of second-order weighted elliptic operators in divergence form in the plane to a singular elliptic operator with a second order fractal term.
An example of fractal singular homogenization / U., Mosco; Vivaldi, Maria Agostina. - In: GEORGIAN MATHEMATICAL JOURNAL. - ISSN 1072-947X. - STAMPA. - 14 n°1:(2007), pp. 169-193.
An example of fractal singular homogenization
VIVALDI, Maria Agostina
2007
Abstract
We construct a sequence of quadratic weighted energy forms in an open domain of the plane, which M-converges to the an energy form with a singular fractal term. The weights belong to the A_2-Muckenoupt class and have point-wise singularities. The result implies the spectral convergence of a sequence of second-order weighted elliptic operators in divergence form in the plane to a singular elliptic operator with a second order fractal term.File | Dimensione | Formato | |
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