engleski

H-distributions in various settings

H-distributions were recently introduced as an extension of H-measures to the ${; ; ; \rm L}; ; ; ^p-{; ; ; \rm L}; ; ; ^q$ setting. As classical Tartar's H-measures (and similar objects independently introduced by G\'erard under the name of microlocal defect measures), they are microlocal defect functionals defined on the tensor product of test functions in the physical variable ${; ; ; \bf x}; ; ; \in{; ; ; \bf R}; ; ; ^d$ and the dual variable ${; ; ; \boldsymbol \xi}; ; ; \in{; ; ; \rm S}; ; ; ^{; ; ; d-1}; ; ; $. The original construction can be extended to mixed-norm Lebesgue spaces, with a potential for further extension to Sobolev spaces modelled either over classical or mixed-norm Lebesgue spaces, or in the anisotropic direction as it was done for H-measures, depending on what might be required by intended applications. For all above variants a localisation principle can be established, providing applications in the theory of partial differential equations like compactness by compensation for equations with variable coefficients.

H-distribution ; H-measure ; microlocal defect functional

nije evidentirano