# An Obstacle Problem for Elastic Curves: Existence Results

## TL;DR

This paper studies an obstacle problem for elastic curves with fixed endpoints, exploring conditions for existence and nonexistence of solutions, and extending the class of admissible curves using penalization methods.

## Contribution

It introduces a novel approach to extend admissible curves for elastic obstacle problems and establishes existence results via penalization, addressing nonexistence cases.

## Key findings

- Identifies conditions under which graph solutions do not exist.
- Extends the class of admissible curves for the problem.
- Provides an existence proof using penalization techniques.

## Abstract

We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of admissible curves in a way that an existence result can be obtained by a penalization argument.