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

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 Fréchet 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. [ABSTRACT FROM AUTHOR]