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The convex envelope is the solution of a nonlinear obstacle problem
Author(s):
Adam
M.
Oberman
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1689-1694.
MSC (2000):
Primary 35J70, 52A41;
Secondary 93E20, 65N06
Posted:
February 7, 2007
MathSciNet review:
2286077
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Additional information
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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MSC (2000):
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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:
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
Posted:
February 7, 2007
Additional Notes:
It is a pleasure to acknowledge Luis Silvestre for valuable discussions.
Communicated by:
Walter Craig
Copyright of article:
Copyright
2007,
American Mathematical Society
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