The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
Analysis of PDEs
2023-10-03 v1 Numerical Analysis
Numerical Analysis
Abstract
This article is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between Banach spaces near branches of isolated solutions that are implicitly defined by a residual equation. Under -Gevrey assumptions on on the residual equation, we establish -Gevrey bounds on the Fr\'echet derivatives of the local data-to-solution mapping. This abstract framework is illustrated in a proof of regularity bounds for a semilinear elliptic partial differential equation with parametric and random field input.
Keywords
Cite
@article{arxiv.2310.01256,
title = {The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs},
author = {Helmut Harbrecht and Marc Schmidlin and Christoph Schwab},
journal= {arXiv preprint arXiv:2310.01256},
year = {2023}
}