Showing papers by "Aldo Pratelli published in 2016"
TL;DR: In this article, the authors considered the Cheeger problem for non-convex domains, with a particular interest in the case of planar strips, which have been extensively studied in recent years.
Abstract: In this paper we consider the Cheeger problem for non-convex domains, with a particular interest in the case of planar strips, which have been extensively studied in recent years. Our main results are an estimate on the Cheeger constant of strips, which is stronger than the previous one known from Krejciřik and Pratelli (Pac J Math 254(2):309–333, 2011), and the proof that strips share with convex domains a number of crucial properties with respect to the Cheeger problem. Moreover, we present several counterexamples showing that the same properties are not valid for generic non-convex domains.
50 citations
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TL;DR: In this article, the authors considered the mass transport problem in the case of a relativistic cost, and established the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under mild assumptions.
Abstract: In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under mild assumptions. These results generalize those recently obtained by J.Bertrand, A.Pratelli and M.Puel, also positively answering some of the open questions there.
3 citations