The property of compactness of the quasi-linearly perturbed harmonic-map equation

G. Yu Kokarev

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

For maps u: M ? M' of closed Riemannian manifolds a study is made of the quasi-linearly perturbed harmonic-map equation t(u)(x) = G(x, u(x)) · du(x) + g(x, u(x)), x ? M. In the case of a non-positively curved manifold M' and a small linear part of the perturbation G it is proved that the space of classical solutions in a fixed homotopy class is compact. The proof is based on a uniform estimate for the norm of the differential of a solution of the perturbed equation in terms of its energy and the C1norms of G and g. The crux of this analysis is an inequality called the monotonicity property.

Original languageEnglish
Pages (from-to)1055-1068
Number of pages14
JournalSbornik: Mathematics
Volume194
Issue number7-8
Publication statusPublished - Jul 2003

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