PhD thesis:
Title : Discontinuous Hamilton-Jacobi equations and parabolic regularity à la De Giorgi
Advisor : Cyril Imbert
Date of defense : June 26, 2018
Preprint:
J. Guerand, Quantitative regularity for parabolic De Giorgi classes, HAL (2020). Links: hal, arxiv
F. Anceschi, H. Dietert, J. Guerand, A. Loher, C. Mouhot, A. Rebucci, Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators (2024). Link: arxiv
J. Guerand, C. Imbert, C. Mouhot, Gehring's Lemma for kinetic Fokker-Planck equations (2024). Links: arxiv, hal
Publications :
J. Guerand, Flux-limited solutions and state constraints for quasi-convex Hamilton-Jacobi equations in multidimensional domains, Nonlinear Analysis (2017). Links : Journal, hal, arxiv
J. Guerand, Effective nonlinear Neumann boundary conditions for 1D nonconvex Hamilton–Jacobi equations, Journal of Differential Equation (2017). Links : Journal, hal, arxiv
J. Guerand, M. Koumaiha, Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction, Numerische Mathematik (2019). Liens: Journal, pdf, hal, arxiv
J. Guerand, C. Imbert, Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations, Journal of the Institute of Mathematics of Jussieu (2021). Links: hal, arxiv
J. Guerand, C. Mouhot, Quantitative De Giorgi Methods in kinetic theory, Journal de l'École Polytechnique (2021). Links: Journal
J. Guerand, A. Menegaki, A. Trescases, Global existence for triangular reaction cross-diffusion systems. Bulletin des sciences mathématiques (2023). Links: arxiv, hal
J. Guerand, M. Hillairet, S. Mirrahimi, A moment-based approach for the analysis of the infinitesimal model in the regime of small variance, Kinetic and Related Models (2024). Links: arxiv, hal
L. Alasio, J. Guerand, S. Schulz, Regularity and trend to equilibrium for a non-local advection-diffusion model of active particles, Kinetic and Related Models (2024). Links: arxiv, hal