Weak approximation by bounded Sobolev maps with values into complete manifolds |
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Authors: | Pierre Bousquet Augusto C. Ponce Jean Van Schaftingen |
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Affiliation: | 1. Université de Toulouse, Institut de mathématiques de Toulouse, UMR CNRS 5219, Université Paul-Sabatier Toulouse 3, 118 route de Narbonne, 31062 Toulouse Cedex 9, France;2. Université catholique de Louvain, Institut de recherche en mathématique et physique, chemin du cyclotron 2, bte L7.01.02, 1348 Louvain-la-Neuve, Belgium |
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Abstract: | We have recently introduced the trimming property for a complete Riemannian manifold as a necessary and sufficient condition for bounded maps to be strongly dense in when . We prove in this note that, even under a weaker notion of approximation, namely the weak sequential convergence, the trimming property remains necessary for the approximation in terms of bounded maps. The argument involves the construction of a Sobolev map having infinitely many analytical singularities going to infinity. |
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