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quasiconvex duality

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Duality for the level sum of quasiconvex functions and applications
M. Volle
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 3 / 1998

Published online by Cambridge University Press:

15 August 2002, pp. 329-343

Print publication:

1998
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We study a quasiconvex conjugation that transforms the level sum of functions into the pointwise sum of their conjugates and derivenew duality results for the minimization of the max of two quasiconvex functions. Following Barron and al., we show that the levelsum provides quasiconvex viscosity solutions for Hamilton-Jacobi equations in which the initial condition is a general continuousquasiconvex function which is not necessarily Lipschitz or bounded.