<p>We introduce classes of microlocal compactness wave front variants. In some sense, they measure how far a sequence bounded in a Sobolev space is from being relatively compact in that space. We distinguish local and nonlocal variants. In applications, we give their basic properties and also a connection with H-measures introduced independently by Luc Tartar and Patrick Gérard.</p>

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Microlocal compactness wave fronts in Sobolev spaces

  • Ivan Ivec,
  • Ivana Vojnović

摘要

We introduce classes of microlocal compactness wave front variants. In some sense, they measure how far a sequence bounded in a Sobolev space is from being relatively compact in that space. We distinguish local and nonlocal variants. In applications, we give their basic properties and also a connection with H-measures introduced independently by Luc Tartar and Patrick Gérard.