TITLE

# Example of a displacement convex functional of first order

AUTHOR(S)
Carrillo, José A.; Slepčev, Dejan
PUB. DATE
December 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Dec2009, Vol. 36 Issue 4, p547
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We present a family of first-order functionals which are displacement convex, that is convex along the geodesics induced by the quadratic transportation distance on the circle. The displacement convexity implies the existence and uniqueness of gradient flows of the given functionals. More precisely, we show the existence and uniqueness of gradient-flow solutions of a class of fourth-order degenerate parabolic equations with periodic boundary data. Moreover, positivity of the absolutely continuous part of the solutions is preserved along the flow.
ACCESSION #
44753948

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