The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
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Date
2023-10Type
- Report
ETH Bibliography
yes
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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 \(s\)-Gevrey assumptions on on the residual equation, we establish \(s\)-Gevrey bounds on the Fréchet 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. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Implicit mappings; Parametric regularity; Uncertainty quantification; Semilinear elliptic PDEsOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Related publications and datasets
Is previous version of: https://doi.org/10.3929/ethz-b-000666889
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ETH Bibliography
yes
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