engleski

Some-generalisations of H-measures

H-measures were defined independently by Luc Tartar and Patrick Gerard, as objects measuring the lack of strong convergence in weakly converging sequences in L^2(R^d ; R^r). They are Radon measures defined on R^d x S^(d-1), their existence relying on the First commutation lemma (as it was baptised by Tartar). They have already found a number of applications to hyperbolic and elliptic partial differential equations. Recently, Nenad Antonić and Marin Lazar introduced parabolic H-measures for application to parabolic problems, showing their feasibility to the main types of applications, as they were known for the classical H-measures. Our goal is to provide a systematic approach to this and other possible extensions, with an ultimate goal of tailoring the variants appropriate for applications in various classes of partial differential equations. We also provide some general variants of the first commutation lemma.

H-measures ; generalisations ; first commutation lemma

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