University of Jyväskylä

Dissertation: 16.12 On generalizations of Evans and Gangbo´s approximation method and L∞ optimal transport (Jylhä)

Start date: Dec 16, 2014 12:00 AM

End date: Dec 16, 2014 03:00 PM

Location: Mattilanniemi, MaA211

Heikki Jylhä. Kuvaaja: Sanna Vatanen.M.Sc. Heikki Jylhä defends his doctoral dissertation in Mathematics. Opponent Academy Researcher FT Tuomo Kuusi (Aalto yliopisto) and custos Professor Petri Juutinen (University of Jyväskylä). The event is in Finnish.

Abstract

The thesis consists of two articles, both studying topics in the theory of optimal transportation. The first article generalizes the approximation method by Evans and Gangbo, which they used to solve Monge’s problem. Our article proves that similar approximation using solutions to p-Laplace type problems yields Kantorovich potentials to a certain optimal transport problem, which takes into account the boundary data in p-Laplace type problems. The second article establishes the basic results about L optimal transport. In particular, we use a suitable version of cyclical monotonicity to characterize restrictable solutions and prove that these solutions are induced by transport maps in the Euclidean space provided that the initial measure and the cost function satisfy certain fairly general assumptions.

The dissertation is published in the series University of Jyväskylä, Department of Mathematics and Statistics, Report 146, Jyväskylä 2014, ISSN 1457-8905, ISBN 978-951-39-5967-8. The publication can be inquired from Heikki Jylhä.

  • Further information:

Heikki Jylhä, tel. +358 45 6712467, heikki.j.jylha@ jyu.fi

Communications intern Birgitta Kemppainen, tel. +358 40 805 4483, tiedotus@jyu.fi