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The quasiconvex envelope through first-order partial differential equations which characterize quasiconvexity of nonsmooth functions
Discrete and continuous dynamical systems. Series B
Dedicated to Avner Friedman on his 80th birthday. Abstract. Necessary and sufficient conditions for quasiconvexity, also called level-set convexity, of a function are given in terms of first-order partial differential equations. Solutions to the equations are understood in the viscosity sense and the conditions apply to nonsmooth and semicontinuous functions. A comparison principle, implying uniqueness of solutions, is shown for a related partial differential equation. This equation is thendoi:10.3934/dcdsb.2012.17.1693 fatcat:dduwfjwlzbe3bax3hiipbn6owa