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 .
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 .
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@article{CRMATH_2004__339_12_855_0, author = {Poliakovsky, Arkady}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2004.09.030/} }
TY - JOUR AU - Poliakovsky, Arkady TI - On a minimization problem related to lifting of BV functions with values in $ {S}^{1}$ JO - Comptes Rendus. Mathématique PY - 2004 SP - 855 EP - 860 VL - 339 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2004.09.030/ DO - 10.1016/j.crma.2004.09.030 LA - en ID - CRMATH_2004__339_12_855_0 ER -
%0 Journal Article %A Poliakovsky, Arkady %T On a minimization problem related to lifting of BV functions with values in $ {S}^{1}$ %J Comptes Rendus. Mathématique %D 2004 %P 855-860 %V 339 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2004.09.030/ %R 10.1016/j.crma.2004.09.030 %G en %F CRMATH_2004__339_12_855_0
Poliakovsky, Arkady. On a minimization problem related to lifting of BV functions with values in $ {S}^{1}$. Comptes Rendus. Mathématique, Tome 339 (2004) no. 12, pp. 855-860. doi : 10.1016/j.crma.2004.09.030. http://archive.numdam.org/articles/10.1016/j.crma.2004.09.030/
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