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2001 Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts
Olivier Ley
Adv. Differential Equations 6(5): 547-576 (2001). DOI: 10.57262/ade/1357141855

Abstract

This paper is concerned with first-order time-dependent Hamilton-Jacobi equations. Exploiting some ideas of Barron and Jensen [9], we derive lower-bound estimates for the gradient of a locally Lipschitz-continuous viscosity solution $u$ of equations with a convex Hamiltonian. Using these estimates in the context of the level-set approach to front propagation, we investigate the regularity properties of the propagating front of $u$, namely $\Gamma_t = \{ x \in \mathbb R^n : u(x,t)=0 \}$ for $t \geq 0$. We show that, contrary to the smooth case, such estimates do not guarantee, in general, any expected regularity for $\Gamma_t$ even if $u$ is semiconcave.

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Olivier Ley. "Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts." Adv. Differential Equations 6 (5) 547 - 576, 2001. https://doi.org/10.57262/ade/1357141855

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1015.35031
MathSciNet: MR1826721
Digital Object Identifier: 10.57262/ade/1357141855

Subjects:
Primary: 35F25
Secondary: 35B37 , 49L25

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.6 • No. 5 • 2001
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