• Corpus ID: 235490144

Stability of a class of action functionals depending on convex functions

@inproceedings{Ambrosio2021StabilityOA,
  title={Stability of a class of action functionals depending on convex functions},
  author={Luigi Ambrosio and Camillo Brena},
  year={2021}
}
We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the underlying space. Introduction The aim of this short note is to investigate the stability of action functionals of the form 
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References

SHOWING 1-9 OF 9 REFERENCES
$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions
Given a real function f , the rate function for the large deviations of the diffusion process of drift ∇f given by the Freidlin-Wentzell theorem coincides with the time integral of the energy…
Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
TLDR
A new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound is given.
Gradient flows and Evolution Variational Inequalities in metric spaces. I: Structural properties
Gradient flows on nonpositively curved metric spaces and harmonic maps
The notion of gradient flows is generalized to a metric space setting without any linear structure. The metric spaces considered are a generalization of Hilbert spaces, and the properties of such…
Convex Analysis and Optimization in Hadamard Spaces
This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and…
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence…
Metric Spaces of Non-Positive Curvature
This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by…
The dynamical Schr\"odinger problem in abstract metric spaces
In this paper we introduce the dynamical Schrödinger problem on abstract metric spaces, defined for a wide class of entropy and Fisher information functionals. Under very mild assumptions we prove a…
The dynamical Schrödinger problem in abstract metric spaces, 2020
  • L. Ambrosio: Scuola Normale Superiore, Piazza dei Cavalieri
  • 2020