Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
Analysis of PDEs
2023-05-26 v2 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2305.12202,
title = {Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs},
author = {Jose Pinto and Fernando Henríquez and Carlos Jerez-Hanckes},
journal= {arXiv preprint arXiv:2305.12202},
year = {2023}
}