Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities

Details Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities

2010-12-14

arxiv.org/abs/1012.3087v1

Mathematics

Analysis of PDEs

Submitted, 2010

Scientific paper

We consider periodic homogenization problems for the L{\'e}vy operators with asymmetric L{\'e}vy densities. The formal asymptotic expansion used for the $\a$-stable (symmetric) L{\'e}vy operators ($\a\in (0,2)$) is not applicable directly to such asymmetric cases. We rescale the asymmetric densities, extract the most singular part of the measures, which average out the microscopic dependences in the homogenization procedures. We give two conditions (A) and (B), which characterize such a class of asymmetric densities, that the above "rescaled" homogenization is available.

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