Weak Comparison Principles for Fully Nonlinear Degenerate Parabolic Equations with Discontinuous Source Terms
Keywords:
Weak comparison principle, viscosity solution, fully nonlinear equation, discontinuous source term, level-set mean curvature flow equation.Abstract
We study the initial value problem for a fully nonlinear degenerate parabolic equation with discontinuous 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 curvature 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.
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