# Transportation of measures through branched networks at finite cost

## Eugene Stepanov (St. Petersburg State University)

created by gelli on 23 Nov 2007

28 nov 2007

Abstract.

Sala Riunioni--Dipartimento di Matematica--ore 17.00

Eugene Stepanov (Univ. San Pietroburgo) Transportation of measures through branched networks at finite cost''

ABSTRACT: The following transportation problem is studied: characterize those couples of finite Borel measures with compact supports in a Euclidean space that can be transported to each other at a finite fractional cost, given by a fractional mass of real one-dimensional normal currents. Besides the class of irrigable measures (i.e. measures which can be transported to a Dirac measure with the appropriate total mass at a finite cost), two other important classes of measures related to the problem are studied which in a certain sense are complementary to each other.

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