A class of elliptic equations related to optical design

We use a local geometric construction to derive a class of elliptic differential operators. The requirement that the operator will be a derivative of a functional leads to a natural characterization of a family of operators that connect the classical Laplace operator to the mean curvature operator. We further show that the elliptic operators derived here have a canonical interpretation in the framework of optical design.

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Published 1 January 2002