# Some analytic results on interpolating sesqui-harmonic maps

## TL;DR

This paper investigates the mathematical properties of interpolating sesqui-harmonic maps between Riemannian manifolds, focusing on spherical targets, deriving conservation laws, and establishing smoothness and classification results.

## Contribution

It provides new analytic insights into interpolating sesqui-harmonic maps, including conservation laws and smoothness criteria, especially for spherical targets.

## Key findings

- Derived a conservation law for interpolating sesqui-harmonic maps.
- Proved smoothness of weak solutions in the spherical case.
- Classified certain interpolating sesqui-harmonic maps.

## Abstract

In this article we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that interpolates between the functionals for harmonic and biharmonic maps. In the case of a spherical target we will derive a conservation law and use it to show the smoothness of weak solutions. Moreover, we will obtain several classification results for interpolating sesqui-harmonic maps.