On introduit une relation d'équivalence sur liée au degré topologique, et on présente des estimées pour les distances (au sens usuel et au sens de Hausdorff) entre les classes d'équivalence. Dans certains cas particuliers, il s'agit même de formules exactes. On considère ensuite des questions semblables pour .
We introduce an equivalence relation on involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases, we even obtain exact formulas. Next we discuss related issues for .
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@article{CRMATH_2016__354_7_677_0, author = {Br\'ezis, Ha{\"\i}m and Mironescu, Petru and Shafrir, Itai}, title = {Distances between classes of sphere-valued {Sobolev} maps}, journal = {Comptes Rendus. Math\'ematique}, pages = {677--684}, publisher = {Elsevier}, volume = {354}, number = {7}, year = {2016}, doi = {10.1016/j.crma.2016.05.001}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2016.05.001/} }
TY - JOUR AU - Brézis, Haïm AU - Mironescu, Petru AU - Shafrir, Itai TI - Distances between classes of sphere-valued Sobolev maps JO - Comptes Rendus. Mathématique PY - 2016 SP - 677 EP - 684 VL - 354 IS - 7 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.05.001/ DO - 10.1016/j.crma.2016.05.001 LA - en ID - CRMATH_2016__354_7_677_0 ER -
%0 Journal Article %A Brézis, Haïm %A Mironescu, Petru %A Shafrir, Itai %T Distances between classes of sphere-valued Sobolev maps %J Comptes Rendus. Mathématique %D 2016 %P 677-684 %V 354 %N 7 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.05.001/ %R 10.1016/j.crma.2016.05.001 %G en %F CRMATH_2016__354_7_677_0
Brézis, Haïm; Mironescu, Petru; Shafrir, Itai. Distances between classes of sphere-valued Sobolev maps. Comptes Rendus. Mathématique, Tome 354 (2016) no. 7, pp. 677-684. doi : 10.1016/j.crma.2016.05.001. http://www.numdam.org/articles/10.1016/j.crma.2016.05.001/
[1] Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal., Volume 80 (1988), pp. 60-75
[2] H. Brézis, P. Mironescu, Sobolev maps with values into the circle, Birkhäuser, in preparation.
[3] -maps with values into , Geometric Analysis of PDE and Several Complex Variables, Contemp. Math., vol. 368, American Mathematical Society, Providence, RI, USA, 2005, pp. 69-100
[4] H. Brézis, P. Mironescu, I. Shafrir, Distances between classes in , in preparation.
[5] Distances between homotopy classes of , ESAIM Control Optim. Calc. Var. (2016) (in press, hal-01257581)
[6] Degree theory and BMO. I. Compact manifolds without boundaries, Sel. Math. New Ser., Volume 1 (1995), pp. 197-263
[7] On the distance between homotopy classes of maps between spheres, J. Fixed Point Theory Appl., Volume 15 (2014), pp. 501-518
[8] The distance between homotopy classes of -valued maps in multiply connected domains, Isr. J. Math., Volume 160 (2007), pp. 41-59
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