References & Citations
Mathematics > Analysis of PDEs
Title: Hamilton-Jacobi equations with monotone nonlinearities on convex cones
(Submitted on 25 Jun 2022 (v1), last revised 16 Nov 2023 (this version, v3))
Abstract: We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the well-posedness of the equation in the viscosity sense and prove several properties of the solution: monotonicity, Lipschitzness, and representations by variational formulas.
Submission history
From: Hong-Bin Chen [view email][v1] Sat, 25 Jun 2022 02:31:43 GMT (30kb,D)
[v2] Fri, 5 Aug 2022 21:25:09 GMT (31kb,D)
[v3] Thu, 16 Nov 2023 12:24:05 GMT (31kb,D)
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