# On boundary detachment phenomena for the total variation flow with dynamic boundary conditions

## TL;DR

This paper investigates how facets detach at boundaries in the total variation flow with dynamic boundary conditions, especially focusing on radially symmetric data and boundary layer detachment at concave boundary parts.

## Contribution

It combines total variation flow with dynamic boundary conditions and analyzes boundary facet detachment phenomena, highlighting effects at concave boundary regions.

## Key findings

- Boundary layer detachment can occur at concave boundary parts.
- Facets behavior at boundary is significantly influenced by dynamic boundary conditions.
- Radially symmetric data simplifies the analysis of boundary phenomena.

## Abstract

We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the boundary where these conditions are imposed. We devote particular attention to the radially symmetric data. We observe that the boundary layer detachment actually can happen at concave parts of the boundary