Differential and Integral Equations

Semicontinuous viscosity solutions for Hamilton-Jacobi equations with a degenerate coefficient

Shigeaki Koike

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Abstract

The Hamilton-Jacobi equation with concave Hamiltonians and degenerate coefficients is treated. A new definition of viscosity solutions is proposed to deal with lower semicontinuous solutions. Under the setting, the comparison principle for lower semicontinuous viscosity solutions is established. The justification of our definition in applications is shown.

Article information

Source
Differential Integral Equations, Volume 10, Number 3 (1997), 455-472.

Dates
First available in Project Euclid: 2 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367525662

Mathematical Reviews number (MathSciNet)
MR1744856

Zentralblatt MATH identifier
0890.35064

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

Citation

Koike, Shigeaki. Semicontinuous viscosity solutions for Hamilton-Jacobi equations with a degenerate coefficient. Differential Integral Equations 10 (1997), no. 3, 455--472. https://projecteuclid.org/euclid.die/1367525662


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