Forthcoming book:
An Illustrated Guide of the Modern Approches of Hamilton-Jacobi Equations and Control Problems with Discontinuities, with G. Barles — 2019 preliminary version here: (pdf)

1
Preprints (2019)

  1. Sharp estimates of the generalized principal eigenvalue for superlinear viscous Hamilton-Jacobi equations with inward drift, with N. Ichihara — preprint (2019) — (pdf)

2
Published in 2019

  1. A priori Lispschitz estimates for solutions of local and nonlocal Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator, with O. Ley and T.T. Nguyen — Revista Matematica Iberoamericana 35 (5) (2019), 1415-1449 — (pdf)
  2. Ergodic Problems for Viscous Hamilton-Jacobi Equations with Inward Drift, with N. Ichihara — SIAM Journal on Control and Optimization 57 (2019), 23-52. (pdf)
  3. On unbounded solutions of ergodic problems for non-local Hamilton–Jacobi equations, with C. Brandle — Nonlinear Analysis 180 (2019), 94-128 — (pdf)

2
Published in 2018

  1. Flux-limited and classical viscosity solutions for regional control problems, with G. Barles, A. Briani, and C. Imbert — ESAIM Control Optim. Calc. Var., 24 (2018), 1881-1906 — (pdf)

2
Published in 2017

  1. Corrigendum to " (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains ", with G. Barles — (pdf)
  2. On nonlocal quasilinear equations and their local limits, with E. Jakobsen — J. Differential Equations 262 (2017), 3759-3804 — (pdf)

3
Published in 2016

  1. Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations, with N. Ichihara — NoDEA 23 (2016), 1-17 — (pdf)
  2. On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations., with G. Barles — Journal of Differential Equations 260(9) (2016), 7020-7031 — (pdf)

4
Published in 2015

  1. (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains, with G. Barles, Networks and heterogenous media 10 (2015), 809-836 — (pdf) — Corrigendum: (hal)
  2. An homogeneization result for a multi-domains periodic problem, with G. Barles, A. Briani and N. Tchou, Asymptotic Analysis 95 (2015), 243-278 — (pdf)

5
Published in 2014

  1. A Bellman approach for regional optimal control problems in $R^N$, with A. Briani and G. Barles, Siam Journal on Control and Optimization, 52 (2014) 1712--1744 — (pdf)
  2. Isothermalisation for a nonlocal heat equation, with R. Ferreira, Ann. Sc. Norm. Super. Pisa Cl. Sci. 13 (2014), 1-18 — (pdf)
  3. On Neumann-type problems for nonlocal equations set in a half space, with G. Barles, C. Georgelin and E. Jakobsen, Trans. Amer. Math. Soc. 366 (2014), 4873--4917. — (pdf)
  4. Fractional decay bounds for nonlocal zero order heat equations, with P. Felmer, J.D. Rossi, and E. Topp, Bull. London Math. Soc. 46 (2014), 943-952 — (pdf)
  5. Large time behavior of periodic viscosity solutions for integro-differential equations, with G. Barles, A. Ciomaga and C. Imbert, Calc. Var. Partial Differential Equations 50 (2014), no. 1-2, 283-304 — (pdf)

6
Published in 2013

  1. A nonlocal two-phase Stefan problem, with S. Sastre-Gomez, Diff. Int. Equations 26 (2013), 1235-1434 – (pdf)
  2. A Bellman approach for two-domains optimal control problems in $R^N$, with A. Briani and G. Barles, ESAIM Control Optim. Calc. Var. 19 (2013), 710-739. – (pdf)
  3. Large Deviations estimates for some non-local equations. General bounds and applications, with C. Brändle, Trans. Amer. Math. Soc. 365 (2013), 3437-3476 – (pdf)

7
Published 2008-2012

  1. Phase transitions with midrange interactions: a nonlocal Stefan model, with C. Brändle and F. Quiros, SIAM J. Math. Anal. 44 (2012), no. 4, 3071-3100 – (pdf)
  2. Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations, with G. Barles, A. Ciomaga and C. Imbert, J. Differential Equations 252 (2012), no. 11, 6012-6060 – (pdf)
  3. Unbounded solutions of the nonlocal heat equation, with C. Brändle and R. Ferreira, Commun. Pure Appl. Anal. 10 (2011), no. 6, 1663–1686 – (pdf)
  4. Hölder continuity of solutions of second-order non-linear elliptic integro-differential equation, with G. Barles and C. Imbert, J.E.M.S. 13 (2011) 1-26 – (pdf)
  5. Large Deviations estimates for some non-local equations I. Fast decaying kernels and explicit bounds, with C. Brändle, Nonlinear Analysis TMA 71 (2009), 5572-5586 – (pdf)
  6. On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations, with G. Barles and C. Imbert, Indiana Univ. Math. Jl 57, 1 (2008) 213-146 – (pdf)

8
Published 2000-2008

  1. The Dirichlet problem for some non-local diffusion equations, Differential Integral Equations 20 (2007), no. 12, 1389–1404.
  2. Asymptotic behavior for nonlocal diffusion equations, with M. Chaves and J.D. Rossi, J. Math. Pures Appl. (9) 86 (2006), no. 3, 271–291.
  3. Extended solutions for general fast diffusion equa- tions with optimal measure data, with J.L. Vazquez, Adv. Differential Equations 11 (2006), no. 6, 627–646.
  4. Monotone approximations of Green’s functions, with R. Ferreira, C. R. Math. Acad. Sci. Paris 339 (2004), no. 6, 395–400.
  5. The pressure equation in the fast diffusion range, with J.L. Vazquez, Rev. Mat. Iberoamericana 19 (2003), no. 3, 873–917.
  6. Fundamental solutions and singular shocks in scalar conservation laws, Rev. Mat. Complut. 16 (2003), no. 2, 443–463
  7. Uniqueness without growth condition for the mean curvature equation with radial initial data, with S. Biton and O Ley, Comm. Partial Differential Equations 28 (2003), no. 9-10, 1503–1526.
  8. Une estimation de type Aronson-Bénilan, C. R. Math. Acad. Sci. Paris 336 (2003), no. 12, 991–996.
  9. Classification of razor blades to the filtration equation — the sublinear case, J. Differential Equations 187 (2003), no. 1, 72–105.
  10. Sets of admissible initial data for porous-medium equations with absorption, with J.L. Vazquez, Proceedings of the 2001 Luminy Conference on Quasilinear Elliptic and Parabolic Equations and System, 53–83 (electronic), Electron. J. Differ. Equ. Conf. 8, Southwest Texas State Univ., San Marcos, TX, 2002.
  11. Initial trace of solutions of some quasilinear parabolic equations with absorption, with L. Véron and M.F. Bidaut-Véron, J. Funct. Anal. 193 (2002), no. 1, 140– 205.
  12. Theory of extended solutions for fast-diffusion equa- tions in optimal classes of data. Radiation from singularities, with J.L. Vazquez, Arch. Ration. Mech. Anal. 164 (2002), no. 2, 133–187.
  13. Initial trace for a porous medium equation. I. The strong absorption case, Ann. Mat. Pura Appl. (4) 179 (2001), 413–458.
  14. Initial trace for a porous medium equation. II. The critical absorption term, Asymptot. Anal. 24 (2000), no. 1, 37–72.

9

I defended my "Habilitation à diriger les recherches" in Oct. 2014.
The complete folder is here.