
Minimax Theory and its Applications 08 (2023), No. 1, 037060 Copyright Heldermann Verlag 2023 Weak Comparison Principles for Fully Nonlinear Degenerate Parabolic Equations with Discontinuous Source Terms Nao Hamamuki Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, Japan hnao@math.sci.hokudai.ac.jp Kuniyasu Misu Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, Japan kuniyasu.misu@math.sci.hokudai.ac.jp 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 levelset 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. Keywords: Weak comparison principle, viscosity solution, fully nonlinear equation, discontinuous source term, levelset mean curvature flow equation. MSC: 35B51, 35D40, 35K15. [ Fulltextpdf (184 KB)] for subscribers only. 