Gradient flows for non-smooth interaction potentials

DOI10.1016/j.na.2014.01.010zbMath1285.49035arXiv1206.4453OpenAlexW2963436153MaRDI QIDQ2442742

Stefano Lisini, Edoardo Mainini, José Antonio Carrillo

Publication date: 1 April 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.4453

zbMATH Keywords

Wasserstein distancegradient flowsaggregation equationsmeasure solutionnonsmooth interaction potentialsWasserstein subdifferential

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) General first-order partial differential equations and systems of first-order partial differential equations (35F99)

Related Items (13)

The Pontryagin Maximum Principle in the Wasserstein space ⋮ On continuity equations in space-time domains ⋮ The Filippov characteristic flow for the aggregation equation with mildly singular potentials ⋮ Mathematical imaging and surface processing. Abstracts from the workshop held August 21--27, 2022 ⋮ Gradient Flows for Probabilistic Frame Potentials in the Wasserstein Space ⋮ Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations ⋮ Gradient flows of time-dependent functionals in metric spaces and applications to PDEs ⋮ Cross-diffusion systems with excluded-volume effects and asymptotic gradient flow structures ⋮ Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels ⋮ Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D ⋮ An invariance principle for gradient flows in the space of probability measures ⋮ A review of the mean field limits for Vlasov equations ⋮ Nonlocal-interaction equations on uniformly prox-regular sets

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