Obstacle problems for the elastic flow and related topics

TL;DR

This paper investigates obstacle problems for elastic flow, establishing local existence of weak solutions and exploring their relation to classical solutions, while also reviewing related obstacle problems for bending energy.

Contribution

It introduces new results on obstacle problems for elastic flow, including existence proofs and connections to classical solutions, expanding understanding of bending energy obstacles.

Findings

Proved local-in-time existence of weak solutions.

Analyzed the relation between weak and classical solutions.

Reviewed related obstacle problems for bending energy.

Abstract

In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when additional regularity is obtained. Related results concerning obstacle problems for the bending energy are also collected.