Weak Comparison Principles for Fully Nonlinear Degenerate Parabolic Equations with Discontinuous Source Terms

We study the initial value problem for a fully nonlinear degenerate parabolic equation with dis-continuous source terms, to which a usual type of comparison principles does not apply. Examples include singular equations appearing in surface evolution problems such as the level-set mean curva-ture flow equation with a driving force term and a discontinuous source term. By a suitable scaling, we establish weak comparison principles for a viscosity sub-and supersolution to the equation. We also present uniqueness and existence results of possibly discontinuous viscosity solutions.