Hamilton-Jacobi equations with monotone nonlinearities on convex cones

Hong-Bin Chen; Jiaming Xia

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arXiv · 2206.12537

Hamilton-Jacobi equations with monotone nonlinearities on convex cones

Hong-Bin Chen·Jiaming Xia

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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.

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Hong-Bin Chen, Jiaming Xia. 2022-06-25. Hamilton-Jacobi equations with monotone nonlinearities on convex cones. https://arxiv.org/abs/2206.12537

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