?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpublications.ut-capitole.fr%2Fid%2Feprint%2F26149%2F&rft.title=A+family+of+functional+inequalities&rft.creator=Blanchet%2C+Adrien&rft.creator=Bolte%2C+J%C3%A9r%C3%B4me&rft.subject=B-+ECONOMIE+ET+FINANCE&rft.description=For+displacement+convex+functionals+in+the+probability+space+equipped+with+the+Monge-Kantorovich+metric+we+prove+the+equivalence+between+the+gradient+and+functional+type+Lojasiewicz+inequalities.+In+a+second+part%2C+we+specialise+these+inequalities+to+some+classical+geodesically+convex+functionals.+For+the+Boltzmann+entropy%2C+we+obtain+the+equivalence+between+logarithmic+Sobolev+and+Talagrand's+inequalities.+On+the+other+hand%2C+the+non-linear+entropy+and+the+Gagliardo-Nirenberg+inequality+provide+a+Talagrand+inequality+which+seems+to+be+a+new+equivalence.+Our+method+allows+also+to+recover+some+results+on+the+asymptotic+behaviour+of+the+associated+gradient+flows.&rft.publisher=IAST+Working+Paper&rft.date=2017-03&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpublications.ut-capitole.fr%2Fid%2Feprint%2F26149%2F1%2FIAST_V1%2Fwp%2Fwp_iast_1766.pdf&rft.identifier=++Blanchet%2C+Adrien+%3Chttps%3A%2F%2Fwww.idref.fr%2F12046246X%3E+and+Bolte%2C+J%C3%A9r%C3%B4me+%3Chttps%3A%2F%2Fwww.idref.fr%2F078638623%3E++(2017)++A+family+of+functional+inequalities%3A+lojasiewicz+inequalities+and+displacement+convex+functions.+IAST+Working+Paper%2C+n.+17-66%2C+Toulouse+++++&rft.relation=http%3A%2F%2Fiast.fr%2Fpub%2F31597&rft.language=en