Intrinsic semiharmonic maps

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For maps from a domain $\Omega \subset \mathbb{R}^m$ into a Riemannian manifold $N$, a functional coming from the norm of a fractional Sobolev space has recently been studied by Da Lio and Rivière. An intrinsically defined functional with a similar behavior also exists, and its first variation can be identified with a Dirichlet-to-Neumann map belonging to the harmonic map problem. The critical points have regularity properties analogous to harmonic maps.
Original languageEnglish
Pages (from-to)588-598
Number of pages11
JournalJournal of Geometric Analysis
Issue number3
Publication statusPublished - 2011


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