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arXiv · 1609.05681

H-distribution via Sobolev spaces

Jelena Aleksic·Stevan Pilipovic·Ivana Vojnovic
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Abstract

H-distributions associated to weakly convergent sequences in Sobolev spaces are determined. It is shown that a weakly convergent sequence $(u_n)$ in $W^{-k,p}( \R^d)$ has the property that $\theta u_n$ converges strongly in $W^{-k,p}(\R^d)$ for every $\theta\in\mathcal S(\R^d)$ if and only if all H-distributions related to this sequence are equal to zero. Results are applied on a weakly convergent sequence of solutions to a family of linear first order PDEs.

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Jelena Aleksic, Stevan Pilipovic, Ivana Vojnovic. 2016-09-19. H-distribution via Sobolev spaces. https://arxiv.org/abs/1609.05681

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