TY - JOUR
T1 - Intrinsic semiharmonic maps
AU - Moser, Roger
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80051800556&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s12220-010-9159-7
U2 - 10.1007/s12220-010-9159-7
DO - 10.1007/s12220-010-9159-7
M3 - Article
SN - 1050-6926
VL - 21
SP - 588
EP - 598
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -