Convergence of minimizers for the \(p\)-Dirichlet integral (Q1320998)

The introduction: The purpose of this paper is to show that a weakly convergent sequence of minimizing \(p\)-harmonic maps, \(\infty > p > 1\), between Riemannian manifolds converges to a minimizing \(p\)-harmonic map. For special target manifolds this has been proved by \textit{R. Hardt} and \textit{F. H. Lin} [Commun. Pure Appl. Math. 40, 555-588 (1987; Zbl 0646.49007), Theorem 6.4]; and if the domain is a ball, it has been proved by the author [Indiana Univ. Math. J. 37, No. 2, 349-368 (1988; Zbl 0641.58012)], and indeed used crucially in the blow up argument of that paper. The proof given here is a straightforward generalization of the latter method. The result is stated for more general functionals and problems with constraints, as it does not complicate the proof.