Équation de la chaleur pour les applications p-harmoniques entre variétés riemanniennes compactes

Abstract

Let (M^m,g) and (Nⁿ,h) (m⩾2) be two compact Riemannian manifolds without boundary. When Riem_N⩽0, we show the global existence of a weak solution of the heat equation for p-harmonic maps (p>1) and the convergence of this solution at infinity to a regular weakly p-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that p>1.