The convex envelope is the solution of a nonlinear obstacle problem

Oberman, Adam

doi:10.1090/S0002-9939-07-08887-9

The convex envelope is the solution of a nonlinear obstacle problem
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Proc. Amer. Math. Soc. 135 (2007), 1689-1694 Request permission

Abstract:

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.

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