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Computing the convex envelope using a nonlinear partial differential equation. (English) Zbl 1154.35056

The paper is concerned with the study of the numerical solving with a finite difference method, of the convex envelope using a fully nonlinear partial differential equation. In one dimension, this equation is reduced to the classical obstacle problem. It provides a local characterization of the convex envelope, that allows numerical methods to be constructed which involve only local conditions, eliminating costly global constrains. The scheme is shown to converge and the computational results for smooth and nonsmooth data are presented.

MSC:

35J70 Degenerate elliptic equations
26B25 Convexity of real functions of several variables, generalizations
52A41 Convex functions and convex programs in convex geometry
65N06 Finite difference methods for boundary value problems involving PDEs

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References:

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