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arXiv · 2510.00146

Classification of solutions of an elliptic Hamilton-Jacobi equation

Alessio Porretta·Philippe Souplet
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Abstract

We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation $-\Delta u= |\nabla u|^p$ in a half-space with zero boundary conditions for $1 2$, our result completes the full classification picture of the Dirichlet problem for equation (DHJ) in a half-space.

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Alessio Porretta, Philippe Souplet. 2025-09-30. Classification of solutions of an elliptic Hamilton-Jacobi equation. https://arxiv.org/abs/2510.00146

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