Motion of sets by curvature and derivative of capacity potential

TL;DR

This paper investigates a geometric flow influenced by boundary curvature and capacity potential derivatives, establishing local existence and weak formulations for handling singularities.

Contribution

It introduces a novel curvature-capacity driven flow, proving local well-posedness and proposing weak formulations to extend solutions beyond singularities.

Findings

Proved local well-posedness of the flow.

Developed two weak formulations for singularities.

Extended the flow beyond initial singularities.

Abstract

We study a geometric flow where the motion of a set is driven by the mean curvature of its boundary and the normal derivative of its capacity potential. We establish local well-posedness and propose two possible weak formulations that exist after singularities.