Resolvent Flows for Convex Functionals and p-Harmonic Maps

Kazuhiro Kuwae

Analysis and Geometry in Metric Spaces, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces.

Détail

Publié le : 2015-01-01

Zbl 1314.53071

EUDML-ID : urn:eudml:doc:270015

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