Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow

By Luigi Ambrosio, Myriam Lecumberry, Stefania Maniglia. 2005

67 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/eb033ab1bec3874f748f7d50197bf68c2a3e874d

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Citations in the corpus

Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves (2020, methodology): “5 employ all some suitable Lusin-Lipschitz type estimates for u, an idea pioneered in [5] and [14] and which has proved quite fruitful in different contexts (see for instance [6–8,13,16]).”
Estimates and regularity results for the DiPerna-Lions flow (2008, methodology): “[5] Ambrosio, L.; Lecumberry, M.; Maniglia, S. Lipschitz regularity and approximate differentiability of the DiPerna–Lions flow.”
Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows (2018, result): “The first result in this direction was obtained by Crippa–De Lellis in [28], building upon some ideas that have appeared in [11].”
The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems (2011, methodology): “However, the way we derive our estimates is different: our analysis relies all on the Lagrangian formulation, whereas that of [19] relies on the Eulerian one.”
Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients (2008, unknown): “The generalization of the results of the present work to drift vectors b that are BV functions, in the spirit of the works [1, 2, 3, 13], is an interesting open question.”
Differential equations with singular fields (2010, background): “Some information of this kind can still be derived, for instance by studying the differentiability or approximate differentiability of the flow as in [3], [6].”