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This paper is about elliptic and parabolic partial differential operatorswith discontinuities in the gradient which are compatible with a Finsler normin a sense to be made precise. Examples of this type of problems arise in anumber of contexts, most notably the recent work of Chatterjee and the secondauthor [7] on scaling limits of discrete surface growth models as well as$L^{\infty}-$variational problems. Building on the approach of Ishii [16], newcomparison results are proven within a unified framework that includes a numberof previous results as special cases.

Comparison Principles for Second Order Elliptic/Parabolic Equations with Discontinuities in the Gradient Compatible with Finsler Norms