Extensions of divergence-free fields in L¹-based function spaces

2024/08/08 by Franz Gmeineder, Gmeineder, Franz, Stefan Schiffer +1
Economics, Econometrics and Finance · Mathematics · #26B20 #35D30 #46E40 #53A05 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2408.04513

openalex publication_date 2024/08/08 · openalex created_date 2024/11/01 · openalex updated_date 2026/07/28

Abstract

We establish the first extension results for divergence-free (or solenoidal) elements of L¹-based function spaces. Here, the key point is to preserve the solenoidality constraint while simultaneously keeping the underlying L¹-boundedness. While previous results as in Kato et al. [Extension and representation of divergence-free vector fields on bounded domains, Math. Res. Lett., 2000] for L^p-based function spaces, 1

Related

• Dimension reduction for functionals on solenoidal vector fields
• Construction of function spaces close to L^∞ with associate space close to L¹
• Two Approximation Results for Divergence Free Measures
• Operator gradient of divergencie in subspaces of L₂(G) space
• Shadowing, expansiveness and stability of divergence-free vector fields