# Total energy of radial mappings

## TL;DR

This paper extends a key result by proving that the total energy functional for radial mappings between annuli reaches its minimum on a diffeomorphism, involving analysis of a special ODE.

## Contribution

It generalizes previous work by establishing the existence of a minimal total energy radial diffeomorphism between annuli.

## Key findings

- Total energy functional attains minimum on a radial diffeomorphism.
- Involves analysis of a specific ordinary differential equation.
- Extends prior results to a broader class of mappings.

## Abstract

The main aim of this paper is to extend one of the main results of Iwaniec and Onninen (Arch. Ration. Mech. Anal., 194: 927-986, 2009). We prove that, the so called total energy functional defined on the class of radial streachings between annuli attains its minimum on a total energy diffeomorphism between annuli. This involves a subtle analysis of some special ODE.