Convex extension preserving Lipschitz constant

[摘要] Let Omega subset of R-n be a non-empty bounded open and convex set and let f be a real function defined on the boundary of the set Omega. A necessary and sufficient condition is given for f to be extendable to a convex and lipschitzian function defined on the whole space R-n. The solution u to the degenerate case of the Monge-Ampere equation det[partial derivative(2)u/partial derivative x(f) partial derivative x(f)] = 0, u = f on the boundary of Omega, is lipschitzian if and only if f satisfies this condition. (C) 1997 academic Press.

[发布日期] 1997-08-01