The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation

By Ugo Gianazza, Giuseppe Savar'e, Giuseppe Toscani. 2009

188 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cb49645458561ea65e483690b74dcd8aa0846aab

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In Applied Mathematics

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Citations in the corpus

On the Bakry-\'Emery condition, the gradient estimates and the Local-to-Global property of RCD*(K,N) metric measure spaces (2013, unknown): “Analogous results (in X = Rd) when only a one-sided bound on f is available have been proved with completely different proofs in [24, 20].”
Free boundaries in optimal transport and Monge-Ampere obstacle problems (2010, background): “Agueh [2], Ambrosio, Gigli and Savare [8], Cullen and Gangbo [29], Gianazza, Savare and Toscani [45], Savin [71]; in shape optimization since the work of Bouchitte, Buttazzo and Seppecher [11], see also e.”
The Pontryagin Maximum Principle in the Wasserstein Space (2017, unknown): “[14, 27]).”
A Family of Nonlinear Fourth Order Equations of Gradient Flow Type (2009, methodology): “The situation α = 1/2 has been discussed by Gianazza, Savaré and Toscani [24].”
Computational Optimal Transport (2018, methodology): “JKO flows can be used to study in particular nonlinear evolution equations such as the porous medium equation [Otto, 2001], total variation flows [Carlier and Poon, 2019], quantum drifts [Gianazza et al., 2009], or heat evolutions on manifolds [Erbar, 2010].”
On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of $$\mathsf{RCD}^*(K,N)$$RCD∗(K,N) Metric Measure Spaces (2016, result): “Analogous results (in X = Rd) when only a one-sided bound on f is available have been proved with completely different proofs in [24, 20].”
On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics (2008, background): “A partial result on this limit was given by Jüngel, Li and Matsumura in [26], while in [22] it is shown the global existence of non-negative variational solutions to (14) without the electrostatic potential and the pressure term.”
Nonlinear mobility continuity equations and generalized displacement convexity (2009, methodology): “Since H is nonnegative, the smoothness and convexity of Ω and the smoothness of ζ yields, see [24,25,34], ∇|∇ζ |2 · n 0, on ∂Ω, ∫”