-
Previous Article
Large time behavior for a nonlocal nonlinear gradient flow
- DCDS Home
- This Issue
-
Next Article
An $ L^{q}\rightarrow L^{r} $ estimate for rough Fourier integral operators and its applications
Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.
Readers can access Online First articles via the “Online First” tab for the selected journal.
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. |
| [1] |
Augusto Visintin. $ \Gamma $-compactness and $ \Gamma $-stability of the flow of heat-conducting fluids. Discrete and Continuous Dynamical Systems - S, 2022, 15 (8) : 2331-2343. doi: 10.3934/dcdss.2022066 |
| [2] |
Martin Heida, Stefan Neukamm, Mario Varga. Stochastic homogenization of $ \Lambda $-convex gradient flows. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 427-453. doi: 10.3934/dcdss.2020328 |
| [3] |
Luca Battaglia, Francesca Gladiali, Massimo Grossi. Asymptotic behavior of minimal solutions of $ -\Delta u = \lambda f(u) $ as $ \lambda\to-\infty $. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 681-700. doi: 10.3934/dcds.2020293 |
| [4] |
Harun Karsli, Purshottam Narain Agrawal. Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation. Mathematical Foundations of Computing, 2022 doi: 10.3934/mfc.2022002 |
| [5] |
Lingyan Cheng, Ruinan Li, Liming Wu. Exponential convergence in the Wasserstein metric $ W_1 $ for one dimensional diffusions. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5131-5148. doi: 10.3934/dcds.2020222 |
| [6] |
Federico Rodriguez Hertz, Zhiren Wang. On $ \epsilon $-escaping trajectories in homogeneous spaces. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 329-357. doi: 10.3934/dcds.2020365 |
| [7] |
Teresa Alberico, Costantino Capozzoli, Luigi D'Onofrio, Roberta Schiattarella. $G$-convergence for non-divergence elliptic operators with VMO coefficients in $\mathbb R^3$. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 129-137. doi: 10.3934/dcdss.2019009 |
| [8] |
Antonio G. García. Sampling in $ \Lambda $-shift-invariant subspaces of Hilbert-Schmidt operators on $ L^2(\mathbb{R}^d) $. Mathematical Foundations of Computing, 2021, 4 (4) : 281-297. doi: 10.3934/mfc.2021019 |
| [9] |
Pak Tung Ho. Prescribing $ Q $-curvature on $ S^n $ in the presence of symmetry. Communications on Pure and Applied Analysis, 2020, 19 (2) : 715-722. doi: 10.3934/cpaa.2020033 |
| [10] |
Yamin Wang. On nonexistence of extremals for the Trudinger-Moser functionals involving $ L^p $ norms. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4257-4268. doi: 10.3934/cpaa.2020191 |
| [11] |
Yishui Wang, Dongmei Zhang, Peng Zhang, Yong Zhang. Local search algorithm for the squared metric $ k $-facility location problem with linear penalties. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2013-2030. doi: 10.3934/jimo.2020056 |
| [12] |
Yeping Li, Jie Liao. Stability and $ L^{p}$ convergence rates of planar diffusion waves for three-dimensional bipolar Euler-Poisson systems. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1281-1302. doi: 10.3934/cpaa.2019062 |
| [13] |
Jennifer D. Key, Bernardo G. Rodrigues. Binary codes from $ m $-ary $ n $-cubes $ Q^m_n $. Advances in Mathematics of Communications, 2021, 15 (3) : 507-524. doi: 10.3934/amc.2020079 |
| [14] |
Jong Yoon Hyun, Yoonjin Lee, Yansheng Wu. Connection of $ p $-ary $ t $-weight linear codes to Ramanujan Cayley graphs with $ t+1 $ eigenvalues. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020133 |
| [15] |
Umberto De Maio, Peter I. Kogut, Gabriella Zecca. On optimal $ L^1 $-control in coefficients for quasi-linear Dirichlet boundary value problems with $ BMO $-anisotropic $ p $-Laplacian. Mathematical Control and Related Fields, 2020, 10 (4) : 827-854. doi: 10.3934/mcrf.2020021 |
| [16] |
Rakesh Nandi, Sujit Kumar Samanta, Chesoong Kim. Analysis of $ D $-$ BMAP/G/1 $ queueing system under $ N $-policy and its cost optimization. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3603-3631. doi: 10.3934/jimo.2020135 |
| [17] |
Chengxiang Wang, Li Zeng, Wei Yu, Liwei Xu. Existence and convergence analysis of $\ell_{0}$ and $\ell_{2}$ regularizations for limited-angle CT reconstruction. Inverse Problems and Imaging, 2018, 12 (3) : 545-572. doi: 10.3934/ipi.2018024 |
| [18] |
Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Convergence of a finite volume scheme for a stochastic conservation law involving a $Q$-brownian motion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1459-1502. doi: 10.3934/dcdsb.2018159 |
| [19] |
Harbir Antil, Mahamadi Warma. Optimal control of the coefficient for the regional fractional $p$-Laplace equation: Approximation and convergence. Mathematical Control and Related Fields, 2019, 9 (1) : 1-38. doi: 10.3934/mcrf.2019001 |
| [20] |
Wenxian Shen, Shuwen Xue. Persistence and convergence in parabolic-parabolic chemotaxis system with logistic source on $ \mathbb{R}^{N} $. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2893-2925. doi: 10.3934/dcds.2022003 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]