2013/10/16 by Martin Lazar, Darko Mitrovic, Lazar, Martin +2 · 1 citation
Computer Science · Mathematics · #34A08 #35A27 #42B37 #46B50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #math.FA #msc:34A08 #msc:35A27 #msc:42B37 #msc:46B50
paper · pdf · doi:10.48550/arxiv.1310.4285
New results concerning $L^s$-velocity averagingm $s\geq 2$ for equations with optimal eough coefficients are added
openalex publication_date 2013/10/16 · arxiv created 2014/02/01 · arxiv updated 2014/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume that (un) is a sequence of solutions to heterogeneous equations with rough coefficients and fractional derivatives, weakly converging to zero in \rm Lp(\Rd+m), with p>1. We prove that the sequence of averaged quantities (∫ ρ(\my) un(\mx,\my) d\my) is strongly precompact in \Ljl\Rd for any ρ∈ \Cc\Rm, provided that restrictive non-degeneracy conditions are satisfied. These are fulfilled for elliptic, parabolic, fractional convection-diffusion equations, as well as for parabolic equations with a fractional time derivative. The main tool that we are using is an adapted version of H-distributions. As a consequence of the introduced methods, we obtain an optimal velocity averaging result in the \LL p, p≥ 2, framework under the standard non-degeneracy conditions, as well as a connection between the H-measures and the H-distributions.