engleski

One-scale H-distributions

Microlocal defect functionals (H-measures, H-distributions, semiclassical measures etc.) are objects which describe the lack of strong compactness for weakly convergent L^p sequences. In contrast to the semiclassical measures, H-measures are not suitable for problems with a characteristic length (e.g.~thickness of a plate). Luc Tartar overcame the mentioned restriction by introducing one-scale H-measures, a generalisation of H-measures with a characteristic length. Moreover, these objects are also an extension of semiclassical measures, being functionals on the space of continuous functions on a compactification of R^d\{; ; 0}; ; . Recently, the localisation principle for one-scale H-measures was improved giving the possibility to obtain compensated compactness for problems with characteristic length [N. Antonić, M. E., M. Lazar, 2014]. Our goal is to extend this construction to L^p framework and introduce an extension of one-scale H-measures, the one-scale H-distributions, following the approach in [N. Antonić, D. Mitrović, 2011] and obtain corresponding localisation principle.

H-measures ; H-distributions ; localisation principle

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