H-distribution via Sobolev spaces

2016/09/19 by J. Aleksić, Aleksic, Jelena, Stevan Pilipović +3
Engineering · Mathematics · #46F25 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1609.05681

openalex publication_date 2016/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 θu_n converges strongly in W^-k,p(\R^d) for every θ∈\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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