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The convex envelope is the solution of a nonlinear obstacle problem. (English) Zbl 1190.35107

Summary: We derive a nonlinear partial differential equation for the convex envelope of a given function. The solution is interpreted as the value function of an optimal stochastic control problem. The equation is solved numerically using a convergent finite difference scheme.

MSC:

35J70 Degenerate elliptic equations
52A41 Convex functions and convex programs in convex geometry
93E20 Optimal stochastic control
65N06 Finite difference methods for boundary value problems involving PDEs
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