Regularity of certain weakly p-harmonic maps into pseudospheres

Abstract

We propose the notion of p-energy for maps u ∈ W1,p(B, Snν ) from a Euclidean disk B into pseudospheres Snν . Critical maps for this functional is defined to be weakly p-harmonic maps into pseudospheres generalizing the weakly harmonic maps, i.e. p = 2, into pseudospheres studied recently by some authors. We first derive an important identity, analogous to the Wente identity. Then, using this identity together with techniques from theory of elliptic systems, we can prove some ε-regularity results for the weakly p-harmonic maps.