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Stability of a class of action functionals depending on convex functions
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
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.
References:
| [1] |
L. Ambrosio, A. Baradat and Y. Brenier,
$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions, Rend. Lincei. Mat. Appl., 32 (2021), 97-108.
doi: 10.4171/RLM/928. |
| [2] |
L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2$^{nd}$ edition, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2008. |
| [3] |
B. Bač ák, Convex Analysis and Optimization in Hadamard Spaces, De Gruyter Series in Nonlinear Analysis and Applications, Berlin, 2014.
doi: 10.1515/9783110361629. |
| [4] |
M. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999.
doi: 10.1007/978-3-662-12494-9. |
| [5] |
G. Clerc, G. Conforti and I. Gentil, On the variational interpretation of local logarithmic Sobolev inequalities, preprint, 2020, arXiv: 2011.05207. |
| [6] |
S. Daneri and G. Savaré, Lecture notes on gradient flows and optimal transport, In London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, 413 (2014), 100–144. |
| [7] |
U. Mayer,
Gradient flows on nonpositively curved metric spaces and harmonic maps, Comm. Anal. Geom., 6 (1998), 199-253.
doi: 10.4310/CAG.1998.v6.n2.a1. |
| [8] |
L. Monsaingeon, L. Tamanini and D. Vorotnikov, The dynamical Schrödinger problem in abstract metric spaces, preprint, 2020, arXiv: 2012.12005. |
| [9] |
M. Muratori and G. Savaré, Gradient flows and evolution variational inequalities in metric spaces. Ⅰ: Structural properties, J. Funct. Anal., 278 (2020), 108347, 67 pp.
doi: 10.1016/j.jfa.2019.108347. |
show all references
References:
| [1] |
L. Ambrosio, A. Baradat and Y. Brenier,
$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions, Rend. Lincei. Mat. Appl., 32 (2021), 97-108.
doi: 10.4171/RLM/928. |
| [2] |
L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2$^{nd}$ edition, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2008. |
| [3] |
B. Bač ák, Convex Analysis and Optimization in Hadamard Spaces, De Gruyter Series in Nonlinear Analysis and Applications, Berlin, 2014.
doi: 10.1515/9783110361629. |
| [4] |
M. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999.
doi: 10.1007/978-3-662-12494-9. |
| [5] |
G. Clerc, G. Conforti and I. Gentil, On the variational interpretation of local logarithmic Sobolev inequalities, preprint, 2020, arXiv: 2011.05207. |
| [6] |
S. Daneri and G. Savaré, Lecture notes on gradient flows and optimal transport, In London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, 413 (2014), 100–144. |
| [7] |
U. Mayer,
Gradient flows on nonpositively curved metric spaces and harmonic maps, Comm. Anal. Geom., 6 (1998), 199-253.
doi: 10.4310/CAG.1998.v6.n2.a1. |
| [8] |
L. Monsaingeon, L. Tamanini and D. Vorotnikov, The dynamical Schrödinger problem in abstract metric spaces, preprint, 2020, arXiv: 2012.12005. |
| [9] |
M. Muratori and G. Savaré, Gradient flows and evolution variational inequalities in metric spaces. Ⅰ: Structural properties, J. Funct. Anal., 278 (2020), 108347, 67 pp.
doi: 10.1016/j.jfa.2019.108347. |
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