The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.

Review

This book is well worth reading, it gives new insights, even given the fact that there has been quite a large number of previous books on harmonic maps. -- Mathematical Reviews "Mathematical Reviews"

It is clear that this book is well worth reading, and that it gives new insights, even given the fact that there has been quite a large number of previous books on harmonic maps. -- Zentralblatt MATH "Zentralblatt MATH"

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