engleski

One-scale H-distributions

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 ${; ; \rm L}; ; ^p$ sequences. In contrast to the semiclassical measures, H-measures are not suitable to treat problems with a characteristic length (e.g.~thickness of a plate), while more recant variants, one-scale H-measures [1, 3], have property of being extension of both H-measures and semiclassical measures. However, H-measures, as well as one-scale H-measures, are adequate only for the ${; ; \rm L}; ; ^2$ framework. As the generalisation of H-measures to the ${; ; \rm L}; ; ^p-{; ; \rm L}; ; ^{; ; p'}; ; $ setting has already been constructed via H-distributions [2], here we introduce objects which extends the notion of one-scale H-measures, {; ; \sl one-scale H-distributions}; ; , as a counterpart of H-distributions with a characteristic length. Moreover, we address some important features and develop the corresponding localisation principle. [1] N. Antonić, M. Erceg, M. Lazar, Localisation principle for one-scale H-measures, arXiv:1504.03956 (2015) 32 pp. [2] N. Antonić, D. Mitrović, H-distributions: an extension of H-measures to an ${; ; \rm L}; ; ^p-{; ; \rm L}; ; ^q$ setting, Abs.~Appl.~Analysis {; ; \bf 2011}; ; Article ID 901084 (2011) 12 pp. [3] L. Tartar, Multi-scale H-measures, Discrete and Continuous Dynamical Systems, S {; ; \bf 8}; ; (2015), 77--90.

H-measures ; H-distributins ; localisation principle ; semiclassical measures ; characteristic length ; Fourier multipliers

nije evidentirano