Pierre Cardaliaguet

Research Papers

Preprints and preliminary versions on HAL

Published (or about to be) articles:

  1. Viscosity solutions for a polymer crystal growth model (with O. Ley and A. Monteillet) To appear in Indiana Univ. Math. J.

  2. Homogenization and enhancement for the G-equation (with J. Nolen and P. Souganidis) To appear in Arch. Rat. Mec. Anal.

  3. Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in $\R^2/\Z^2$. To appear in Ann. I. H. Poincaré - AN.

  4. Hölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equations. (with P. Cannarsa) Communications on Pure and Applied Mathematics 63, 5 (2010), 590-629.

  5. A double obstacle problem arising in differential game theory. J. Math. Anal. Appl. 360 (2009), no. 1, 95--107.

  6. On a continuous time game with incomplete information. (with C. Rainer) Math. Oper. Res. 34 (2009), no. 4, 769—794.

  7. On a differential model for growing sandpiles with non-regular sources. (with P. Cannarsa and C. Sinestrari) Comm. Partial Differential Equations 34 (2009), no. 7-9, 656—675.

  8. Numerical approximation and optimal strategies for differential games with lack of information on one side. Advances in dynamic games and their applications, 159--176, Ann. Internat. Soc. Dynam. Games, 10, Birkhäuser Boston, Inc., Boston, MA, 2009.

  9. Uniqueness results for non-local Hamilton-Jacobi equations. (with G. Barles, O. Ley and A. Monteillet) J. Functional Anal. 257, 5 (2009), 1261-1287.

  10. Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations. (with G. Barles, O. Ley and A. Monteillet) Nonlinear Anal. 71 (2009), no. 7-8, 2801—2810.

  11. A discussion about the homogenization of moving interfaces (with P.-L. Lions, P. Souganidis). J. Math. Pures Appl.} (9) 91 (2009), no. 4, 339—363.

  12. (pdf) Stochastic differential games with asymmetric information (with C. Rainer). Appl Math Optim (2009) 59: 1-36.

  13. (pdf) A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable. To appear in COCV.

  14. (pdf) Global existence results and uniqueness for dislocation equations (with G. Barles, O. Ley and R. Monneau). SIAM J. Math. Anal. 40 (2008), no. 1, 44--69.

  15. Deterministic differential games under probability knowledge of initial condition. (with M. Quincampoix) Int. Game Theory Rev. 10 (2008), no. 1, 1--16.

  16. (pdf)On the energy of a flow arising in shape optimization (with O. Ley). Interfaces and Free Boundaries, 10 (2008), 221–241.

  17. (pdf) Differential games with asymmetric information. SIAM J. Control Optim. 46 (2007), no. 3, 816—838.

  18. (pdf) Representation formulas for differential games with asymmetric information. J. Optim. Theory Appl. 138 (2008), no. 1, 1--16.

  19. (ps)  Non fattening condition for the generalized evolution by mean curvature and applications (with S. Biton and O. Ley). Interfaces Free Bound. 10 (2008), no. 1, 1--14.

  20. Regularity of eikonal equation with Neumann boundary conditions in the plane: application to fronts with nonlocal terms (with C. Marchi), SIAM J. Control Optim. 45 (2006), no. 3, 1017--1038

  21. (dvi) Zero-sum state constraint differential game: existence of a value for Bolza problem (with P. Bettiol and M. Quincampoix), IJGT, V. 34, N. 3, (2006).

  22. Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles.(with P. Cannarsa and E. Giorgieri). Trans. Amer. Math. Soc. 359 (2007), no. 6, 2741-2775.

  23. (pdf) On some flows in shape optimization (with O. Ley). Arch. Ration. Mech. Anal. 183 (2007), no. 1, 21--58.

  24. (pdf) Existence and uniqueness for dislocation dynamics with nonnegative velocity (with O. Alvarez and R. Monneau). Interfaces Free Bound.7 (2005), no. 4, 415--434.

  25. Perimeter estimates for reachable sets of control systems (with P. Cannarsa). J. Convex Anal. 13 (2006), no. 2, 253--267.

  26. (pdf) Viscosity solutions of Hele-Shaw moving boundary problem for power-law fluid (with E. Rouy). SIAM J. Math. Anal. 38 (2006), no. 1, 143--165

  27. (pdf) A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications (with P. Cannarsa, G. Crasta and E. Giorgieri), Calc. Var. Partial Differential Equations 24 (2005), no. 4, 431--457.

  28. (pdf)  Supremal representation of L-infinity functionals (with F. Prinari),  Appl. Math. Optim. 52 (2005), no. 2, 129--141.

  29. (pdf) Nash equilibrium payoffs for nonzero-sum stochastic differential games (with R. Buckdahn and C. Rainer), SIAM J. Control Optim. 43 (2004), no. 2, 624--642.

  30. (pdf) Representation of equilibrium solutions to the table problem for growing sandpiles (with P. Cannarsa),  J. Eur. Math. Soc. (JEMS) 6 (2004), no. 4, 435--464.

  31. Equilibria and strict equilibria of multivalued maps on noninvariant sets. (with G. Gabor and M. Quincampoix) Ann. Pol. Math. 82, No.1, 19-37 (2003)

  32. (dvi) Existence and uniqueness of a Nash equilibrium feedback  for a simple nonzero-sum differential game (with S. Plaskacz), in International J. Game Theory (2003) 32, pp. 33-71.

  33. (ps) Some uniqueness results for Bernoulli interior free boundary problems in convex domains (with R. Tahraoui),  Electronic J. Diff. Eq.,Vol. 2002 (2002), No. 102, pp.1-16.

  34. Equivalence between rank-one convexity and polyconvexity for isotropic sets of $R^{2\times 2}$ (Parts I and II) (with R. Tahraoui), Nonlinear Analysis, Volume 50, Issue 8, (2002), pp. 1179-1239

  35. (ps) On the strict concavity of the harmonic radius in dimension N2 (with R. Tahraoui), J.Math. Pures Appl.., 81 (2002) pp. 223-240.

  36. A representation formula for the mean curvature motion (with R. Buckdahn and M. Quincampoix), in ``SIAM J. Math. Anal." (2002), V. 33, N. 4, pp. 827-846.

  37. On front propagation problems with non local terms (Part II). in `` J. Math. Anal. Appl. '' 260 (2001), pp. 572-601.

  38. On the approximation of front propagation problems with non local terms. (with D. Pasquignon) in `` RAIRO Mathematical Modeling and Numerical Analysis '' Vol. 35, N. 3 (2001), pp. 437-462.

  39. Pursuit differential games with state constraints. (with M. Quincampoix and P. Saint-Pierre) in `` SIAM J. Control and Optimization '' Vol. 39, N. 5 (2001),  pp. 1615-1632.

  40. (ps) Extended Hardy-Littlewood inequalities and applications to the calculus of variations. (with R. Tahraoui) in `` Advances Diff. Eq.'' Volume 5, No. 7-9 (2000) pp: 1091-1138.

  41. Radon-Nikodym theorem in $L^\infty$. (with E.N. Barron and R.R. Jensen) in `` Appl. Math. Opti.'' Volume 42, No 2 (2000) pp: 103-126.

  42. Numerical schemes for discontinuous value functions of optimal control (with M. Quincampoix and P. Saint-Pierre) in `` Set-valued Analysis '' Vol. 8, N. 1 & 2 (2000) pp: 111-126.

  43. Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable hamiltonians. (with S. Plaskacz) in `` SIAM J. Control and Optimization '' Vol. 38, N.5 (2000) pp: 1501-1520.

  44. (ps) On front propagation problems with non local terms. in `` Advances Diff. Eq.'' Vol. 5, N. 1-3, (2000) pp:213-268.

  45. Geometric restriction for the existence of viscosity solutions. (with B. Dacorogna, W. Gangbo and N. Georgy) in `` Annales de l'I.H.P., Anal. Non Lineaire '' Vol. 6, N. 2 (1999) pp: 189-220.

  46. Numerical methods for differential games. (with M. Quincampoix and P. Saint-Pierre) in `` Stochastic and differential games : Theory and numerical methods '' (1999) pp. 177-247. Annals of the international Society of Dynamic Games, M. Bardi, T.E.S. Raghavan, T. Parthasarathy Eds. Birkh\"{a}user.

  47. Optimal times for constrained nonlinear control problems without local controllability. (with M. Quincampoix and P. Saint-Pierre) in `` Appl. Math. Opti.'' Vol. 36 (1997) pp: 21-42.

  48. On the regularity of Semi-Permeable Surfaces in Control Theory with application to the optimal exit-time problem (Part I and II) in `` SIAM J. Control and Optimization '' Vol. 35, N. 5 (1997) pp: 1638-1671.

  49. Nonsmooth semi-permeable barriers, Isaacs' equation, and application to a differential game with one
    target and two players, in  ``Appl. Math. Opti.",  36, 125-146.

  50. A differential game with two players and one target ``SIAM J. Control and Optimization", Vol. 34, N. 4 (1996)
    pp. 1441-1460.

  51. Some Algorithms for Differential Games with two Players and one Target (with M. Quincampoix and P. Saint-Pierre), in `` RAIRO Mathematical Modeling and Numerical Analysis '', Vol. 28, N. 4,  pp. 441-461.



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