Transport Equation and Cauchy Problem for Non-Smooth Vector Fields

By Luigi Ambrosio. 2008

243 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbd42106e8cde11ce6d143f569e97e47949d402b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Michael Röckner
2. Pierre-Emmanuel Jabin
3. Xicheng Zhang
4. Dario Trevisan
5. Giuseppe Da Prato
6. Alessio Porretta
7. Gianluca Crippa
8. Diogo A. Gomes

In Control and Systems Engineering

1. Dario Trevisan
2. Pierre-Emmanuel Jabin
3. Gianluca Crippa
4. Giuseppe Da Prato
5. Michael Röckner
6. Rinaldo M. Colombo
7. Vladimir Bogachev
8. Diogo A. Gomes

In Mathematical Physics

1. Dario Trevisan
2. Michael Röckner
3. Giuseppe Da Prato
4. Vladimir Bogachev
5. Pierre-Emmanuel Jabin
6. Diogo A. Gomes
7. Alessio Porretta
8. João Saúde

Citations in the corpus

• The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems (2011, methodology): “We also refer to [9], [10] and [79] for an account of the proof of Ambrosio’s theorem.”
• Control of the Continuity Equation with a Non Local Flow (2009, result): “The next lemma is similar to other results in recent literature, see for instance [2].”
• A review of the mean field limits for Vlasov equations (2014, background): “We finally refer to [3] and [50] for a more precise presentation of this subject.”
• A NONLINEAR PARABOLIC-HYPERBOLIC SYSTEM FOR CONTACT INHIBITION OF CELL-GROWTH (2012, background): “expresses his gratitude to Roberto Natalini for indicating the review papers [3] and [10] and to Camillo De Lellis for clarifying some issues related to transport equations.”
• Lagrangian flows for vector fields with gradient given by a singular integral (2012, background): “For a detailed account on these results, we suggest for instance [2, 3, 13, 16].”
• On the Loss of Continuity for Super-Critical Drift-Diffusion Equations (2012, background): “It does not directly cover the case p ∈ [1, 2] in Theorem 1.”
• Existence and uniqueness of solutions for Fokker–Planck equations on Hilbert spaces (2009, background): “[1], [2], [21], [22], [19], [20] and the references therein and also the fundamental paper [18]).”
• Mean Field Games Models—A Brief Survey (2013, methodology): “Consequently, to establish uniqueness, one needs to use a approach due to Ambrosio [5, 6], as explained in detail in [20].”