Geodesic
Resolvent Flows for Convex Functionals and p-Harmonic Maps
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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.
Mots-clés : CAT(0)-space, CAT(k)-space, p-uniformly convex space, weak convergence, p-uniformly λ-convexfunction, Moreau-Yosida approximation, Hamilton-Jacobi semi-group, Hopf-Lax formula, resolvent, localslope, global slope, stationary point, Cheeger’s energy, Cheeger type Sobolev space, p-harmonic map, Lp-Wasserstein space, generalized geodesics 
@article{AGMS_2015_3_1_a18,
     author = {Kuwae, Kazuhiro},
     title = {Resolvent {Flows} for {Convex} {Functionals} and {p-Harmonic} {Maps}},
     journal = {Analysis and Geometry in Metric Spaces},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2015},
     zbl = {1314.53071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a18/}
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Kuwae, Kazuhiro. Resolvent Flows for Convex Functionals and p-Harmonic Maps. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a18/