Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-24T17:12:49.241Z Has data issue: false hasContentIssue false

Homogenizations of integro-differential equations with Lévy operators with asymmetric and degenerate densities

Published online by Cambridge University Press:  20 September 2012

Mariko Arisawa*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK ([email protected])

Abstract

We consider periodic homogenization problems for Lévy operators with asymmetric Lévy densities. The formal asymptotic expansion used for the α-stable (symmetric) Lévy operators (α ∈ (0, 2)) is not directly applicable to such asymmetric cases. We rescale the asymmetric densities and extract the most singular parts of the measures, which average out the microscopic dependencies in the homogenization procedures. We give two conditions, (A) and (B), that characterize such a class of asymmetric densities under which the above ‘rescaled’ homogenization is available.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)