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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The convex envelope is the solution of a nonlinear obstacle problem


Author: Adam M. Oberman
Journal: Proc. Amer. Math. Soc. 135 (2007), 1689-1694
MSC (2000): Primary 35J70, 52A41; Secondary 93E20, 65N06
Published electronically: February 7, 2007
MathSciNet review: 2286077
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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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Additional Information

Adam M. Oberman
Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: aoberman@sfu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08887-9
PII: S 0002-9939(07)08887-9
Keywords: Convex envelope, obstacle problem, partial differential equation
Received by editor(s): November 29, 2005
Published electronically: February 7, 2007
Additional Notes: It is a pleasure to acknowledge Luis Silvestre for valuable discussions.
Communicated by: Walter Craig
Article copyright: © Copyright 2007 American Mathematical Society