# 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} }

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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