2012

Articles

• Bernard, Patrick . The Lax-Oleinik semi-group: a Hamiltonian point of view. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. Volume 142. n° 6. 2012. pages 1131-1177. Royal Society of Edinburgh. DOI http://dx.doi.org/10.1017/S0308210511000059.
• Bernard, Patrick ; Santos, Joana . A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.. Mathematical Proceedings of the Cambridge Philosophical Society. Volume 152. n° 1. 2012. pages 167-178. Cambridge University Press. DOI http://dx.doi.org/10.1017/S0305004111000685.

Conference Contributions

• Bernard, Patrick . Arnold's Diffusion: from the a priori unstable to the a priori stable case.. ICM 2010. Hyderabad. Inde. 2010.
• Bernard, Patrick . Some remarks on the continuity equation. Séminaire: Équations aux Dérivées Partielles. Palaiseau. France. 2012.

Working Papers

• Mandorino, Vito ; Bernard, Patrick . Some remarks on Thom's Transversality Theorem. Université Paris-Dauphine . 2012 .
• Zavidovique, Maxime ; Bernard, Patrick . Regularization of subsolutions in discrete weak KAM theory. Université Paris-Dauphine . 2012 .

2010

Articles

• Bernard, Patrick . Large Normally Hyperbolic Cylinders in a priori Stable Hamiltonian Systems. Annales Henri Poincaré. Volume 11. n° 5. 2010. pages 929-942. Springer. DOI http://dx.doi.org/10.1007/s00023-010-0040-9.
• Bernard, Patrick . On the Number of Mather Measures of Lagrangian Systems. Archive for Rational Mechanics and Analysis. Volume 197. n° 3. 2010. pages 1011-1031. Springer. DOI http://dx.doi.org/10.1007/s00205-009-0289-7.
• Santos, Joana ; Bernard, Patrick . A geometric definition of the Aubry-Mather set. Journal of Topology and Analysis. Volume 2. n° 3. 2010. pages 385-393. world scientific pub.. DOI http://dx.doi.org/10.1142/S1793525310000343.
• Bernard, Patrick . On the Conley decomposition of Mather sets. Revista Matematica Iberoamericana. Volume 26. n° 1. 2010. pages 115-132.
• Bernard, Patrick ; Bessi, Ugo . Young measures, Cartesian maps, and polyconvexity. Journal of the Korean Mathematical Society. Volume 47. n° 2. 2010. pages 331-350. Korean Mathematical Society.
• Bernard, Patrick . Lasry-Lions regularization and a Lemma of Ilmanen. Rendiconti del Seminario Matematico della Università di Padova. Volume 124. 2010. pages 221-229. Universita di Padova.

2008

Articles

• Bernard, Patrick ; Ambrosio, Luigi . Uniqueness of signed measures solving the continuity equation for Osgood vector fields. Rendiconti Lincei - Matematica E Applicationi. Volume 19. n° 3. 2008. pages 237--245.
• Bernard, Patrick . The dynamics of pseudographs in convex Hamiltonian systems. Journal of the American Mathematical Society. Volume 21. n° 3. 2008. pages 615-669. AMS. DOI http://dx.doi.org/10.1090/S0894-0347-08-00591-2.
• Bernard, Patrick . Young measures, superposition and transport. Indiana University Mathematics Journal. Volume 57. n° 1. 2008. pages 247-276. Bloomington, Ind.. DOI http://dx.doi.org/10.1512/iumj.2008.57.3163.
• Contreras, Gonzalo ; Bernard, Patrick . A generic property of families of Lagrangian systems. Annals of Mathematics. Volume 167. n° 3. 2008. pages 1099-1108. Princeton University and the Institute for Advanced Study.

2007

Articles

• Bernard, Patrick . Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds. Annales scientifiques de l'Ecole normale supérieure. Volume 40. n° 3. 2007. pages 445-452. Elsevier. DOI http://dx.doi.org/10.1016/j.ansens.2007.01.004.
• Bernard, Patrick ; Buffoni, Boris . Optimal mass transportation and Mather theory. Journal of the European Mathematical Society. Volume 9. n° 1. 2007. pages 85-121. European Mathematical Society. DOI http://dx.doi.org/10.4171/JEMS/74.
• Bernard, Patrick . Smooth critical sub-solutions of the Hamilton-Jacobi equation. Mathematical research letters. Volume 14. n° 3. 2007. pages 503-511. International Press.
• Bernard, Patrick ; Buffoni, Boris . Weak KAM pairs and Monge-Kantorovich duality. advances studies in pure mathematics. Volume 47. n° 2. 2007. pages 397-420. AMS.

2006

Articles

• Bernard, Patrick ; Buffoni, Boris . The Monge problem for supercritical Mane potentials on compact manifolds. Advances in Mathematics. Volume 207. n° 2. 2006. pages 691-706. Elsevier. DOI http://dx.doi.org/10.1016/j.aim.2006.01.003.

Book chapters

• Bernard, Patrick . Hamiltonian Systems: Stability and Instability Theory. J.-P. Francoise, G.L. Naber and Tsou S.T.. Encyclopedia of Mathematical Physics. . 2006.

2003

Articles

• Bernard, Patrick . Homoclinic orbit to a center manifold. Calculus of Variations and Partial Differential Equations. Volume 17. n° 2. 2003. pages 121-157. Springer. DOI http://dx.doi.org/10.1007/s00526-002-0162-0.

2002

Articles

• Bernard, Patrick . Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits. Journal of Differential Equations. Volume 180. n° 2. 2002. pages 427-452. Elsevier. DOI http://dx.doi.org/10.1006/jdeq.2001.4062.

1996

Articles

• Bernard, Patrick . Perturbation d'un hamiltonien partiellement hyperbolique. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. Volume 323. n° 2. 1996. pages 189-194. Elsevier.