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• W2061114984 abstract "Necessary and sufficient conditions for quasiconvexity, also called level-set convexity, of a functionare given in terms of first-order partial differential equations. Solutions to the equationsare understood in the viscosity sense and the conditions apply to nonsmooth and semicontinuousfunctions. A comparison principle, implying uniqueness of solutions, is shown for a relatedpartial differential equation. This equation is then used in an iterative construction ofthe quasiconvex envelope of a function. The results are then extended to robustly quasiconvexfunctions, that is, functions which are quasiconvex under small linear perturbations." @default.
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• W2061114984 date "2012-05-01" @default.
• W2061114984 modified "2023-09-26" @default.
• W2061114984 title "The quasiconvex envelope through first-order partial differential equations which characterize quasiconvexity of nonsmooth functions" @default.
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• W2061114984 doi "https://doi.org/10.3934/dcdsb.2012.17.1693" @default.
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