2020/10/12 by Daniela De Silva, De Silva, Daniela, Giorgio Tortone +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2010.05782
openalex publication_date 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the vectorial analogue of the thin free boundary problem introduced in \citeCRS as a realization of a nonlocal version of the classical Bernoulli problem. We study optimal regularity, nondegeneracy, and density properties of local minimizers. Via a blow-up analysis based on a Weiss type monotonicity formula, we show that the free boundary is the union of a "regular" and a "singular" part. Finally we use a viscosity approach to prove C1,α regularity of the regular part of the free boundary.