Regularity of the p-harmonic maps with potential

Yu-Ming Chu and Xian-Gao Liu

Vol. 237 (2008), No. 1, 45–56

DOI: 10.2140/pjm.2008.237.45

Abstract

The aim of this work is to prove partial regularity of the p-harmonic maps with potential. The main difficultly caused by the potential is in finding the equation satisfied by the scaling function, which breaks down the blow-up processing. We directly estimate the Morrey energy to avoid the difficulties caused by blowing up.

Keywords

harmonic map, partial regularity, potential

Mathematical Subject Classification 2000

Primary: 58E20

Secondary: 35J60

Milestones

Received: 9 August 2006

Revised: 13 April 2008

Accepted: 30 April 2008

Published: 1 September 2008