An introduction to H-measures and their applications

Abstract

These notes attempt a simple introduction to H-measures (microlocal defect measures), a tool designed independently by P. Gérard and by L. Tartar to compute weak limits of quadratic products of oscillating fields. The canvas around which the concepts are presented is that of the linear wave equation with smooth coefficients and rapidly oscillating initial data. The weak limit of the energy density is computed and a compactness result of the L6-norm of the field (in ℝ3) at each time is established.