Regularity bounds for a Gevrey criterion in a kernel-based regularization of the Cauchy problem of elliptic equations

TL;DR

This paper establishes regularity bounds for a Gevrey criterion in kernel-based regularization of elliptic Cauchy problems, addressing practical challenges in verifying the criterion, especially with nonlinearities, to enhance real-world application effectiveness.

Contribution

It provides new regularity bounds for the Gevrey criterion in elliptic Cauchy problem regularization, including nonlinear cases, improving practical applicability.

Findings

Derived regularity bounds for the Gevrey criterion.

Addressed verification challenges in regularization methods.

Extended analysis to nonlinear power-law cases.

Abstract

This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit its importance to engineering circumstances. Therefore, coping with that impediment helps us improve the use of some regularization methods in real-world applications. This work also consider the presence of the power-law nonlinearities.