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math.AP2025
Classification of solutions of an elliptic Hamilton-Jacobi equation
Alessio Porretta, Philippe Souplet
We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation in a half-space with zero boundary conditions for is necessarily…
math.AP2025
Classification of entire and ancient solutions of the diffusive Hamilton-Jacobi equation
Loth Damagui Chabi, Philippe Souplet
Consider the diffusive HJ eq. with Dirichlet conditions, which arises in stochastic control as well as in KPZ type models of surface growth. It is known that, for and suitabl…
math.AP2025
Optimal Hamilton-type gradient estimates and large time heat kernel bounds for noncompact manifolds
Loth Damagui Chabi, Philippe Souplet
We derive localized and global noncompact versions of Ham\-ilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounde…