Manifold Constrained Variational Problems

@inproceedings{Dacorogna2003ManifoldCV,
  title={Manifold Constrained Variational Problems},
  author={Bernard Dacorogna and Irene Fonseca and Jan Mal{\'y} and Konstantina Trivisa},
  year={2003}
}
The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a C m-dimensional manifold M ⊂ R is obtained. If f : Rd×N → [0,∞) is a continuous function satisfying 0 ≤ f(ξ) ≤ C(1 + |ξ|), for C > 0, p ≥ 1, and for all ξ ∈ Rd×N , then F(u, Ω) : = inf {un}  lim inf n→∞ Z Ω f(∇un) dx : un ⇀ u in W , un(x) ∈M a.e. x ∈ Ω, n ∈ N ff 

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