Orthogonality of H-distributions and applications

Abstract

We extend Gérard's results on orthogonality of ${\mathrm{L}}_{\mathrm{loc}}^2$ sequences as a consequence of mutual singularity of corresponding H-measures (microlocal defect measures) to ${\mathrm{L}}^p$/${\mathrm{L}}^q$ sequences and newly introduced notion of orhogonality for H-distributions. We apply the result to a homogenisation problem for the heterogeneous Boltzmann equation with space-dependent drift and periodic opacity.

15 pages