On obstacle problem for mean curvature flow with driving force

TL;DR

This paper investigates an obstacle problem related to mean curvature flow with a driving force, focusing on regularity, long-term behavior, and characterizing limiting profiles, especially in radially symmetric cases.

Contribution

It provides new regularity results and a detailed analysis of the asymptotic behavior and limiting profiles for the obstacle problem in mean curvature flow with driving force.

Findings

Established interior and boundary regularity of solutions.

Analyzed the large time behavior and convergence of solutions.

Characterized limiting profiles in radially symmetric settings.

Abstract

In this paper, we study an obstacle problem associated with the mean curvature flow with constant driving force. Our first main result concerns interior and boundary regularity of the solution. We then study in details the large time behavior of the solution and obtain the convergence result. In particular, we give full characterization of the limiting profiles in the radially symmetric setting.