Abstract
Let Ω be an open domain in ℝ3 or ℝ4 and N a smooth, compact Riemannian manifold. We consider the Dirichlet energy E(u) for maps u:Ω→N and its negative L2-gradient, the tension field τ(u). We study sequences of maps u
i
:Ω→N with
If the maps are sufficiently regular, we find strong H1-subconvergence away from a generalized submanifold in Ω. If the limit map is regular, too, we can estimate a Willmore-type energy of this generalized submanifold.
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Moser, R. Energy concentration for almost harmonic maps and the Willmore functional. Math. Z. 251, 293–311 (2005). https://doi.org/10.1007/s00209-005-0803-z
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DOI: https://doi.org/10.1007/s00209-005-0803-z