Geodesic
On the duality between $p$-modulus and probability measures
Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 1817-1853

Voir la notice de l'article provenant de la source EMS Press

Motivated by recent developments on calculus in metric measure spaces (X,d,m), we prove a general duality principle between Fuglede's notion [15] of p-modulus for families of finite Borel measures in (X,d) and probability measures with barycenter in Lq(X,m), with q dual exponent of p∈(1,∞). We apply this general duality principle to study null sets for families of parametric and non-parametric curves in X. In the final part of the paper we provide a new proof, independent of optimal transportation, of the equivalence of notions of weak upper gradient based on p-podulus [21, 23] and suitable probability measures in the space of curves ([6, 7]).
DOI : 10.4171/jems/546
Classification : 28-XX, 46-XX, 49-XX
Keywords: p-Modulus, capacity, duality, Sobolev functions 
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Luigi Ambrosio; Simone Di Marino; Giuseppe Savaré. On the duality between $p$-modulus and probability measures. Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 1817-1853. doi: 10.4171/jems/546

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