The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
![Thumbnail](/bitstream/handle/20.500.11850/666889/harbrecht-et-al-2024-the-gevrey-class-implicit-mapping-theorem-with-application-to-uq-of-semilinear-elliptic-pdes.pdf.jpg?sequence=5&isAllowed=y)
Open access
Date
2024-05Type
- Journal Article
ETH Bibliography
yes
Altmetrics
Abstract
This paper 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 s-Gevrey assumptions on the residual equation, we establish s-Gevrey bounds on the Frechet derivatives of the locally defined 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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000666889Publication status
publishedExternal links
Journal / series
Mathematical Models and Methods in Applied SciencesVolume
Pages / Article No.
Publisher
World ScientificSubject
Implicit mappings; parametric regularity; uncertainty quantification; semilinear elliptic PDEsOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Related publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/636052
More
Show all metadata
ETH Bibliography
yes
Altmetrics