Advances in Differential Equations

Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. I. Equations of unbounded and degenerate control problems without uniqueness

Pierpaolo Soravia

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Abstract

We prove general optimality principles for semicontinuous viscosity solutions of Hamilton-Jacobi equations. We also characterize the minimal nonnegative supersolution and the maximal subsolution null on a closed given set for a class of equations without uniqueness, including the degenerate eikonal equation and the Bellman equation of the linear quadratic control problem.

Article information

Source
Adv. Differential Equations, Volume 4, Number 2 (1999), 275-296.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366291416

Mathematical Reviews number (MathSciNet)
MR1674363

Zentralblatt MATH identifier
0955.49016

Subjects
Primary: 49L25: Viscosity solutions
Secondary: 35F20: Nonlinear first-order equations

Citation

Soravia, Pierpaolo. Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. I. Equations of unbounded and degenerate control problems without uniqueness. Adv. Differential Equations 4 (1999), no. 2, 275--296. https://projecteuclid.org/euclid.ade/1366291416


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