Partial regularity for harmonic maps and related problems

By T. Rivière, Michael Struwe. 2006

88 citations recorded by the source corpus.

Via gauge theory, we give a new proof of partial regularity for harmonic maps in dimensions m ≥ 3 into arbitrary targets. This proof avoids the use of adapted frames and permits us to consider targets of “minimal” C2‐regularity. The proof we present extends to a large class of elliptic systems. © 2007 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e7f4a3268fdfff52a5d70569932ee803d801874

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In Applied Mathematics

1. Katarzyna Mazowiecka
2. Armin Schikorra
3. Giampiero Palatucci
4. E. Lenzmann

In Mathematical Physics

1. Katarzyna Mazowiecka
2. Armin Schikorra
3. E. Lenzmann

Citations in the corpus

• Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, unknown): “The theory has been initiated by Schoen & Uhlenbeck [189], and has been developed at length; we refer to [179] for a comprehensive presentation and a list of references.”
• Fractional div-curl quantities and applications to nonlocal geometric equations (2017, background): “or ΩP := (∇P)PT − PΩPT, div(Pij∇uj) = Pjk (ΩP)ij ·∇uk. Thus, up to a multiplicative Pjk, the right-hand side becomes a div-curl quantity. Continuity of uthen follows essentially from Theorem 1.1, cf. [30]. n-harmonicmapsintohomogeneoustargetmanifolds. H´elein’s regularity argument for harmonic maps ”