Abstract
This paper is about elliptic and parabolic partial differential operators with discontinuities in the gradient which are compatible with a Finsler norm in a sense to be made precise. Examples of this type of problems arise in a number of contexts, most notably the recent work of Chatterjee and the second author [7] on scaling limits of discrete surface growth models as well as L∞−variational problems. Building on the approach of Ishii [16], new comparison results are proven within a unified framework that includes a number of previous results as special cases.
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