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1997 Bounded-from-below viscosity solutions of Hamilton-Jacobi equations
Olivier Alvarez
Differential Integral Equations 10(3): 419-436 (1997).

Abstract

We establish a uniqueness and existence theorem for bounded-from-below viscosity solutions of Hamilton-Jacobi equations of the form $u+H(Du)=f$ in $\mathbb{R}^N$. More precisely, we show that there is a unique solution $u$ such that $u^-$ grows at most linearly, when $f^-$ behaves analogously and when $H$ is convex and nonlinear. We sharpen this result when the behavior of the Hamiltonian is known at infinity. We also discuss some extensions to more general Hamiltonians and to the Dirichlet problem in an unbounded open set.

Citation

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Olivier Alvarez. "Bounded-from-below viscosity solutions of Hamilton-Jacobi equations." Differential Integral Equations 10 (3) 419 - 436, 1997.

Information

Published: 1997
First available in Project Euclid: 2 May 2013

zbMATH: 0890.35026
MathSciNet: MR1744854

Subjects:
Primary: 49L25
Secondary: 35F20

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 3 • 1997
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