The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
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2023-10
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Report
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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.
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published
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2023-36
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Implicit mappings; Parametric regularity; Uncertainty quantification; Semilinear elliptic PDEs
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03435 - Schwab, Christoph / Schwab, Christoph
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