Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Jürgen Jost

Max-Planck-Institut für Mathematik, Leipzig, Germany

jjost@mis.mpg.de

Keywords

  • Mosco convergence
  • Gamma convergence
  • Dirichlet form
  • convex functional
  • generalized harmonic mapping
  • nonpositive curvature
  • weak convergence
  • regularity theory

Mathematics Subject Classification

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

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Suggested citation

J. Jost. “From Linear to Convex.” Journal of Convex Analysis 28 (2021), No. 2, 599–612. https://doi.org/10.68381/jca28034

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