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MiS Preprint

Convergence of nonlinear semigroups under nonpositive curvature

Miroslav Bačák


The present paper is devoted to gradient flow semigroups of convex functionals on Hadamard spaces. 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].

MSC Codes:
46T20, 47H20, 58D07
gradient flow, Mosco convergence, semigroup of nonexpansive maps

Related publications

2015 Repository Open Access
Miroslav Bačák

Convergence of nonlinear semigroups under nonpositive curvature

In: Transactions of the American Mathematical Society, 367 (2015) 6, pp. 3929-3953