Resolvent Flows for Convex Functionals and p-Harmonic Maps

Kazuhiro Kuwae

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 46-72, electronic only
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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Kazuhiro Kuwae. "Resolvent Flows for Convex Functionals and p-Harmonic Maps." Analysis and Geometry in Metric Spaces 3.1 (2015): 46-72, electronic only. <http://eudml.org/doc/270015>.

@article{KazuhiroKuwae2015,
abstract = {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.},
author = {Kazuhiro Kuwae},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {CAT(0)-space; CAT(k)-space; p-uniformly convex space; weak convergence; p-uniformly λ-convex function; Moreau-Yosida approximation; Hamilton-Jacobi semi-group; Hopf-Lax formula; resolvent; local slope; global slope; stationary point; Cheeger’s energy; Cheeger type Sobolev space; p-harmonic map; Lp- Wasserstein space; generalized geodesics; -uniformly convex space; -uniformly -convex function; Hamilton-Jacobi semigroup; local slope; Cheeger's energy; -harmonic map; -Wasserstein space},
language = {eng},
number = {1},
pages = {46-72, electronic only},
title = {Resolvent Flows for Convex Functionals and p-Harmonic Maps},
url = {http://eudml.org/doc/270015},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Kazuhiro Kuwae
TI - Resolvent Flows for Convex Functionals and p-Harmonic Maps
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 46
EP - 72, electronic only
AB - 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.
LA - eng
KW - CAT(0)-space; CAT(k)-space; p-uniformly convex space; weak convergence; p-uniformly λ-convex function; Moreau-Yosida approximation; Hamilton-Jacobi semi-group; Hopf-Lax formula; resolvent; local slope; global slope; stationary point; Cheeger’s energy; Cheeger type Sobolev space; p-harmonic map; Lp- Wasserstein space; generalized geodesics; -uniformly convex space; -uniformly -convex function; Hamilton-Jacobi semigroup; local slope; Cheeger's energy; -harmonic map; -Wasserstein space
UR - http://eudml.org/doc/270015
ER -

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