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Journal of Convex Analysis 28 (2021), No. 2, 599--612
Copyright Heldermann Verlag 2021

From Linear to Convex

Jürgen Jost
Max-Planck-Institut für Mathematik, Leipzig, Germany

Umberto Mosco has developed a powerful theory of variational convergence for convex functionals and sets, or with a different terminology, for Dirichlet forms. Such forms are defined on Hilbert spaces. In this contribution, I shall describe how his theory can be extended from Hilbert spaces to metric spaces that themselves satisfy suitable convexity properties.

Keywords: Mosco convergence, Gamma convergence, Dirichlet form, convex functional, generalized harmonic mapping, nonpositive curvature, weak convergence, regularity theory.

MSC: 58E20, 49J45, 54A20, 31C25, 46E36, 54E35.

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