Hamilton-Jacobi equations with monotone nonlinearities on convex cones
Hongbin Chen, Jiaming Xia · arXiv (Cornell University) · 2022
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.