The quasiconvex envelope through first-order partial differential equations which characterize quasiconvexity of nonsmooth functions

DOI10.3934/dcdsb.2012.17.1693zbMath1252.35121OpenAlexW2061114984MaRDI QIDQ449267

Robert R. Jensen, Rafal Goebel, Emmanuel Nicholas Barron

Publication date: 12 September 2012

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2012.17.1693

zbMATH Keywords

Hamilton-Jacobi equationviscosity solutioncomparison principlequasiconvexitylevel-set convexityquasiconvex envelope

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21)

Related Items (7)

Horizontally quasiconvex envelope in the Heisenberg group ⋮ Characterizations of nonsmooth robustly quasiconvex functions ⋮ Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives ⋮ Computing the level set convex hull ⋮ Second-order characterizations of \(\mathcal{C}^1\)-smooth robustly quasiconvex functions ⋮ A uniqueness result for the quasiconvex operator and first order PDEs for convex envelopes ⋮ Convex and quasiconvex functions in metric graphs

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