The Trudinger type inequality in fractional boundary Hardy inequality

2024/10/25 by Adimurthi, Prosenjit Roy, Roy, Prosenjit +2
Mathematics · #26D15 (Secondary) #46E35 (Primary) #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2410.19362

openalex publication_date 2024/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish Trudinger-type inequality in the context of fractional boundary Hardy-type inequality for the case sp=d, where p>1, ~ s ∈ (0,1) on a bounded Lipschitz domain Ω⊂ ℝ^d. In particular, we establish fractional version of Trudinger-type inequality with an extra singular function, namely d-th power of the distance function from ∂ Ω in the denominator of the integrand. The case d=1, as it falls in the category sp=1, becomes more delicate where an extra logarithmic correction is required together with subtraction of an average term.

Related

• Boundary fractional Hardy's inequality in dimension one: The critical case
• Fractional boundary Hardy inequality for the critical cases
• Fractional Hardy inequality with singularity on submanifold
• Critical and subcritical fractional Trudinger-Moser type inequalities on ℝ
• Boundary Hardy inequality on functions of bounded variation