The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs

The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs

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...

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Veröffentlicht in:arXiv.org 2023-10
Hauptverfasser: Harbrecht, Helmut, Schmidlin, Marc, Schwab, Christoph
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Banach spaces
Fields (mathematics)
Mapping
Operators (mathematics)
Partial differential equations
Regularity
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Schwab, Christoph
description 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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subjects Banach spaces
Fields (mathematics)
Mapping
Operators (mathematics)
Partial differential equations
Regularity
title The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
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