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Resolvent Flows for Convex Functionals and p-Harmonic Maps

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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.
Twórcy
  • Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto, 860-8555, Japan
Bibliografia
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  • [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_1515_agms-2015-0004
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