2023/05/20 by José R. Pinto, Pinto, Jose, Henríquez, Fernando +2 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2305.12202
openalex publication_date 2023/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting the corresponding boundary value problems as boundary integral equations, we prove that their solutions depend holomorphically upon perturbations of the arcs' parametrizations. These results are key to prove the shape (domain) holomorphy of the domain-to-solution maps for the associated boundary integral equations with applications in uncertainty quantification, inverse problems and deep learning.