The Partial Regularity Of P-harmonic Heat Flow Equation

This article introduces some basic properties of harmonic map. Then we study the partial regularity of p-harmonic heat flow which has the equation as below:In this article, we prove the decay of the energy, Bochner formula, and the monotonicity formula. By using those theories we can get the partial regularity. To be more precise, if p>2and p-2is sufficiently small, the set of singular points which dimension is n+2-p has limited Hausdoff measure.