For denote by K the set of minimizers of the problem , over satisfying . We show that an extreme point of K must be a lifting of u, up to an additive constant. We also prove a more general result for the case of u in .
Pour on désigne par K l'ensemble des minimiseurs pour le problème sur l'ensemble des fonctions vérifiant . On démontre que chaque point extrême de K est un relèvement de u, à une constante additive près. On démontre ainsi une généralisation pour le cas .
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Arkady Poliakovsky 1
@article{CRMATH_2004__339_12_855_0, author = {Arkady Poliakovsky}, title = {On a minimization problem related to lifting of {BV} functions with values in $ {S}^{1}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {855--860}, publisher = {Elsevier}, volume = {339}, number = {12}, year = {2004}, doi = {10.1016/j.crma.2004.09.030}, language = {en}, }
Arkady Poliakovsky. On a minimization problem related to lifting of BV functions with values in $ {S}^{1}$. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 855-860. doi : 10.1016/j.crma.2004.09.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.030/
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