# A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations

@article{Filippucci2019ALT,
title={A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations},
author={Roberta Filippucci and Patrizia Pucci and Philippe Souplet},
journal={Communications in Partial Differential Equations},
year={2019},
volume={45},
pages={321 - 349}
}
• Published 12 June 2019
• Mathematics
• Communications in Partial Differential Equations
Abstract We consider the elliptic and parabolic superquadratic diffusive Hamilton–Jacobi equations: and with p > 2 and homogeneous Dirichlet conditions. For the elliptic problem in a half-space, we prove a Liouville-type classification, or symmetry result, which asserts that any solution has to be one-dimensional. This turns out to be an efficient tool to study the behavior of boundary gradient blow-up (GBU) solutions of the parabolic problem in general bounded domains of with smooth boundaries…
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