Convergence of nonlinear semigroups under nonpositive curvature

Bačák, Miroslav

doi:10.1090/S0002-9947-2015-06087-5

Convergence of nonlinear semigroups under nonpositive curvature
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Trans. Amer. Math. Soc. 367 (2015), 3929-3953 Request permission

Abstract:

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 the convergence of the corresponding resolvents and the 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. 360, no. 1, 2008].

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