Naslov
Localisation principle for one-scale H-measures

Autori
Antonić, Nenad ; Erceg, Marko ; Lazar, Martin

Izvornik
Journal of functional analysis (0022-1236) 272 (2017), 8; 3410-3454

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Semiclassical measure ; One-scale H-measure ; Localisation principle ; Compactness by compensation

Sažetak
Microlocal defect functionals (H-measures, H-distributions, semiclassical measures etc.) are objects which determine, in some sense, the lack of strong compactness for weakly convergent LpLp sequences. Recently, Luc Tartar introduced one-scale H-measures, a generalisation of H-measures with a characteristic length, which also comprehend the notion of semiclassical measures. We present a self-contained introduction to one-scale H-measures, carrying out some alternative proofs, and strengthening some results, comparing these objects to known microlocal defect functionals. Furthermore, we develop the localisation principle for these objects in a rather general form, from which we are able to derive the known localisation principles for both H-measures and semiclassical measures. Moreover, it enables us to obtain a variant of compactness by compensation suitable for equations with a characteristic length.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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