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Q-valued functions revisited
About this Title
Camillo De Lellis, Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190 CH-8057 Zürich and Emanuele Nunzio Spadaro
Publication: Memoirs of the American Mathematical Society
Publication Year:
2011; Volume 211, Number 991
ISBNs: 978-0-8218-4914-9 (print); 978-1-4704-0608-0 (online)
DOI: https://doi.org/10.1090/S0065-9266-10-00607-1
Published electronically: July 27, 2010
Keywords: $Q$-valued functions; Dirichlet energy; existence and regularity; metric spaces; harmonic maps
MSC: Primary 49Q20, 35J55, 54E40, 53A10
Table of Contents
Chapters
- Introduction
- 1. The elementary theory of $Q$-valued functions
- 2. Almgren’s extrinsic theory
- 3. Regularity theory
- 4. Intrinsic theory
- 5. The improved estimate of the singular set in $2$ dimensions
Abstract
In this note we revisit Almgren’s theory of $Q$-valued functions, that are functions taking values in the space $\mathcal {A}_Q(\mathbb {R}^{n})$ of unordered $Q$-tuples of points in $\mathbb {R}^{n}$. In particular:- Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
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