Orthogonality of H-distributions and applications

TL;DR

This paper generalizes the orthogonality of H-distributions from L^2 sequences to L^p/L^q sequences, introducing a new notion of orthogonality and applying it to a homogenization problem in kinetic theory.

Contribution

It extends Gérard's orthogonality results to broader function spaces and introduces a novel concept of orthogonality for H-distributions, with applications in homogenization of the Boltzmann equation.

Findings

Extended orthogonality results to L^p/L^q sequences.

Introduced a new notion of orthogonality for H-distributions.

Applied the theory to homogenization in kinetic equations.

Abstract

We extend G\'erard's results on orthogonality of ${\rm L}^2_{\rm loc}$ sequences as a consequence of mutual singularity of corresponding H-measures (microlocal defect measures) to ${\rm L}^p$/${\rm L}^q$ 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.