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arXiv:2206.12537 [math.AP]AbstractReferencesReviewsResources

Hamilton-Jacobi equations with monotone nonlinearities on convex cones

Hong-Bin Chen, Jiaming Xia

Published 2022-06-25Version 1

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.

Comments: 30 pages; comments are welcome
Categories: math.AP
Subjects: 35A01, 35A02, 35D40, 35F21
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