Shape Holomorphy of Boundary Integral Operators with Applications to Uncertainty Quantification

Vortrag von Dr. Fernando Henriquez Barraza

Datum: 22.10.25  Zeit: 16.30 - 18.00  Raum: ETH HG G 19.2

We consider a family of boundary integral operators (BIOs) arising from the boundary reduction of well-posed problems—either Laplace or Helmholtz—defined on a collection of parametrically described domains. Our goal is to establish the holomorphic (analytic) dependence of these BIOs, as well as of the solutions to associated boundary integral equations, on perturbations of the domain shape, a property commonly referred to as shape holomorphy. To date, various results have addressed shape holomorphy under differing assumptions, particularly concerning the physical dimension of the problem and, most notably, the smoothness of the domain deformations. In this talk, we present recent results on the shape holomorphy of BIOs under Lipschitz-regular deformations. We also discuss the implications of these findings for the development of computational methods in forward and inverse uncertainty quantification, as well as model order reduction.