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arXiv · 2310.01256

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

Helmut Harbrecht·Marc Schmidlin·Christoph Schwab
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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 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.

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Helmut Harbrecht, Marc Schmidlin, Christoph Schwab. 2023-10-02. The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs. https://arxiv.org/abs/2310.01256

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