Regularity near the fixed boundary for transmission systems

2024/03/07 by Alessio Figalli, Figalli, Alessio, S. Khademloo +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2403.04406

openalex publication_date 2024/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given Ω⊂ ℝⁿ with n≥ 2, D⊂ Ω open, and u:Ω→ ℝ^m, we study elliptic systems of the type \rm div ( ( A + (B- A)χ_D)∇ u) = 0 in Ω∩ B₁, for some uniformly elliptic tensors A and B with Hölder continuous entries. We show that, given appropriate boundary data, the Lipschitz regularity of u inside B₁ ∩ D is transmitted to B_1/2∩ Ω up to the boundary of Ω. This corresponds to the boundary counterpart of the interior regularity results in Figalli-Kim-Shahgholian, Nonlinear Anal. 2022.

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