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.
"Semicontinuous viscosity solutions for Hamilton-Jacobi equations with a degenerate coefficient." Differential Integral Equations 10 (3) 455 - 472, 1997. https://doi.org/10.57262/die/1367525662