On mathematical tools for studying partial differential equations of continuum physics : H-measures and Young measures

摘要

Abstract: u22Some basic results concerning the mathematical tools of Young measures and H-measures are described on a few examples. This includes questions of homogenization, in cases of small amplitude homogenization and in cases where nonlocal effects occur, and questions of propagation of oscillations and concentration effects for a scalar hyperbolic equation and for the wave equation. An application to the relaxation of a functional arising in micromagnetics is given, based on partial knowledge of the relations between Young measures and H-measures.u22