Fractional variable exponents Sobolev trace spaces

2020/08/22 by Mohamed Berghout, Berghout, Mohamed
Mathematics · #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2008.11030

Abstract

We introduce and study fractional variable exponents Sobolev trace spaces on any open set in the Euclidean space equipped with the Lebesgue measure. We show that every equivalence class of Sobolev functions has a quasicontinuous representatives. We use the relative capacity to characterize completely the zero trace fractional variable exponents Sobolev spaces. We also give a relative capacity criterium for removable sets.

Related

• On the Sobolev trace Theorem for variable exponent spaces in the critical range
• Theory of capacities in fracional Sobolev spaces with variable exponents
• Trace of Homogeneous Fractional Sobolev Spaces on Strip-like Domains
• Sobolev trace inequality on W^s,q(ℝⁿ)
• Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents