Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings
نویسنده
چکیده
In this paper we study the lower semicontinuous envelope with respect to the L-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into RN that are constrained to take values into a smooth submanifold Y of RN . Let B be the unit ball in R and Y a smooth Riemannian manifold of dimension M ≥ 1, isometrically embedded in R for some N ≥ 2. We shall assume that Y is compact, connected, without boundary. In this paper we shall be concerned with manifold constrained energy relaxation problems, and we consider variational functionals F : L1(Bn,Y) → [0, +∞] of the type
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