Classification of solutions of an elliptic Hamilton-Jacobi equation

2025/09/30 by Porretta, Alessio, Souplet, Philippe
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.00146

Abstract

We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation -Δu= |∇ u|^p in a half-space with zero boundary conditions for 12, our result completes the full classification picture of the Dirichlet problem for equation (DHJ) in a half-space.

Citations

• Nonlocal Liouville theorems with gradient nonlinearity
• Liouville-type theorems for the Lane-Emden equation in the half-space and cones
• On the Liouville property for fully nonlinear equations with superlinear first-order terms
• Liouville results and asymptotics of solutions of a quasilinear elliptic equation with supercritical source gradient term
• Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Global and local behavior of positive solutions of nonlinear elliptic equations

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• Analysis of the attainment of boundary conditions for a nonlocal\n diffusive Hamilton-Jacobi equation