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

DOI10.1080/03605302.2019.1684941zbMath1436.35010arXiv1906.05161OpenAlexW2990389561MaRDI QIDQ4960225

Roberta Filippucci, Philippe Souplet, Patrizia Pucci

Publication date: 9 April 2020

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05161

zbMATH Keywords

Bernstein-type estimatesloss of boundary conditionsfinal profile

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Hamilton-Jacobi equations (35F21) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (14)

A note on one-dimensional symmetry for Hamilton-Jacobi equations with extremal Pucci operators and application to Bernstein type estimate ⋮ Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms ⋮ Global existence and blow-up of solutions to a parabolic nonlocal equation arising in a theory of thermal explosion ⋮ Asymptotic stability of explicit blowup solutions for three-dimensional incompressible magnetohydrodynamics equations ⋮ A nonlinear elliptic problem involving the gradient on a half space ⋮ Singularity formation and regularization at multiple times in the viscous Hamilton–Jacobi equation ⋮ Beyond the classical strong maximum principle: sign-changing forcing term and flat solutions ⋮ Monotone continuous dependence of solutions of singular quenching parabolic problems ⋮ On a class of nonlinear evolution inequalities of convolution type on Riemannian manifolds ⋮ Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations ⋮ Gradient blowup behavior for a viscous Hamilton-Jacobi equation with degenerate gradient nonlinearity ⋮ Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem ⋮ Monotonicity of solutions for fractional \(p\)-equations with a gradient term ⋮ Complete classification of gradient blow-up and recovery of boundary condition for the viscous Hamilton-Jacobi equation

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