Gradient estimation of a p-harmonic map

Abstract

This article presents L^p estimates for the gradient of p-harmonic maps. Since the system satisfies a natural growth condition, it is difficult to use standard elliptic estimates. We use spherical coordinates to convert the system into another system with angle functions. The new system can be estimate by the standard elliptic technique.

Keywords

• Gradient estimate
• p-harmonic map
• spherical coordinates