Regularity Theory for Harmonic Maps

Abstract

Suppose that Ω is an open subset of ℝⁿ, n ≥ 2, and that N is a smooth compact Riemannian manifold of dimension m ≥ 2 which is isometrically embedded in some Euclidean space ℝ^p. We look at maps u of Ω into N; such a map will always be thought of as a map u = (u¹,…, u^p): Ω → ℝ^p with the additional property that u(Ω) ⊂ N.