P. Bernard

Statistical and Nonlinear Physics · 2004–2016

A researcher in the Science corpus: 6 papers; trusts 13 researchers and is trusted by 22 researchers here, as inferred from the citation graph.

Subfields

• Statistical and Nonlinear Physics — 19 citations into it; #1,689 of 10,127 by trust here, #5,625 by citations
• Applied Mathematics — 15 citations into it; #1,301 of 7,620 by trust here, #2,192 by citations
• Mathematical Physics — 14 citations into it; #3,647 of 8,562 by trust here, #6,594 by citations
• Geometry and Topology — 13 citations into it; #2,034 of 7,422 by trust here, #2,293 by citations
• Computational Theory and Mathematics — 5 citations into it

Whom P. Bernard trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. A. Fathi
2. G. Contreras
3. Luigi Ambrosio
4. Cédric Villani
5. Yann Brenier
6. Gabriel P. Paternain
7. Piermarco Cannarsa
8. K. Siburg
9. Jun Yan
10. Antonio Siconolfi

Who trusts P. Bernard overall

1. Vadim Kaloshin
2. Luigi Ambrosio
3. Shin-ichi Ohta
4. A. Fathi
5. Ke Zhang
6. Giulia Cavagnari
7. Alessio Figalli
8. Andrei A. Agrachev
9. Ludovic Rifford
10. J. Lott

Papers from P. Bernard's perspective

Ordered by how strongly the researchers P. Bernard trusts endorse each paper. Same corpus, a different order for every researcher.

1. Mass transportation problems
2. Existence and stability results in the L 1 theory of optimal transportation
3. Lecture Notes on Optimal Transport Problems
4. Geometric Measure Theory
5. Existence of C1 critical subsolutions of the Hamilton-Jacobi equation
6. Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets
7. Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control
8. Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems
9. Existence of Diffusion Orbits in a priori Unstable Hamiltonian Systems
10. Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems

Their papers

• Young measures, superposition and transport (2007) — 80 citations
• Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders (2016) — 47 citations
• A generic property of families of Lagrangian systems (2008) — 76 citations
• Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds (2005) — 108 citations
• Optimal mass transportation and Mather theory (2004) — 158 citations
• The dynamics of pseudographs in convex Hamiltonian systems (2004) — 138 citations