Convergence of nonlinear semigroups under nonpositive curvature

2012/11/02 by Miroslav Bacak, Bacak, Miroslav · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1211.0414

Accepted for publication in Trans. Amer. Math. Soc

arxiv created 2013/01/24 · arxiv updated 2013/01/25

Abstract

The present paper is devoted to semigroups of nonexpansive mappings on metric spaces of nonpositive curvature. We show that the Mosco convergence of a sequence of convex lsc functions implies convergence of the corresponding resolvents and convergence of the gradient flow semigroups. This extends the classical results of Attouch, Brezis and Pazy into spaces with no linear structure. The same method can be further used to show the convergence of semigroups on a sequence of spaces, which solves a problem of [Kuwae and Shioya, Trans. Amer. Math. Soc., 2008].

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