We study equivalence between the Poincaré inequality and several different relative isoperimetric inequalities on metric measure spaces. We then use these inequalities to establish sufficient conditions for the finite perimeter of sets.
Nous étudions l'équivalence entre l'inégalité de Poincaré et plusieurs différentes inégalités isopérimétriques relatives sur les espaces métriques mesurés. Nous utilisons ensuite ces inégalités afin d'établir des conditions suffisantes sur le périmètre fini d'ensembles.
@article{AIHPC_2014__31_1_129_0, author = {Korte, Riikka and Lahti, Panu}, title = {Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {129--154}, publisher = {Elsevier}, volume = {31}, number = {1}, year = {2014}, doi = {10.1016/j.anihpc.2013.01.005}, mrnumber = {3165282}, zbl = {1285.28003}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.005/} }
TY - JOUR AU - Korte, Riikka AU - Lahti, Panu TI - Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 129 EP - 154 VL - 31 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.005/ DO - 10.1016/j.anihpc.2013.01.005 LA - en ID - AIHPC_2014__31_1_129_0 ER -
%0 Journal Article %A Korte, Riikka %A Lahti, Panu %T Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 129-154 %V 31 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.005/ %R 10.1016/j.anihpc.2013.01.005 %G en %F AIHPC_2014__31_1_129_0
Korte, Riikka; Lahti, Panu. Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 1, pp. 129-154. doi : 10.1016/j.anihpc.2013.01.005. http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.005/
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