Resolvent Flows for Convex Functionals and p-Harmonic Maps

• Autorzy: Kazuhiro Kuwae
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 53C23: Global geometric and topological methods (\`a la Gromov); differential geometric analysis on metric spaces
• 53C20: Global Riemannian geometry, including pinching
• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-07-18

zaakceptowano

2015-01-19

online

2015-02-17

Twórcy

autor

Kazuhiro Kuwae

• Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto, 860-8555, Japan

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0004