Asymptotic analysis of fractional Sobolev spaces on thin films in the low-integrability regime

2025/12/11 by Andrea Braides, Braides, Andrea, Andrea Pinamonti +3
Computer Science · Mathematics · #35R11 #49J45 #73K10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.10620

openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28

Abstract

We study the behaviour of fractional Sobolev spaces H^s(Ω_ε) with s∈(0,1/2) defined on ``thin films'' Ω_ε=ω× (0,ε) in \mathbb R^d, and prove that they tend to the space H^s+\frac12(ω) as ε→ 0. This is made precise by using a notion of dimension-reduction convergence, with respect to which suitably scaled Gagliardo seminorms define equicoercive functionals. Asymptotic results are proved for s→ 0⁺ and s→ 1/2^-.

Citations

• A Bourgain-Brezis-Mironescu result for fractional thin films

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