论文标题
凸锥上具有单调非线性的汉密尔顿 - 雅各比方程
Hamilton-Jacobi equations with monotone nonlinearities on convex cones
论文作者
论文摘要
我们研究了封闭凸锥中的空间变量的汉密尔顿 - 雅各比方程的库奇问题。对非线性的单调性假设使我们能够在圆锥体边界上规定任何条件。我们在粘度意义上显示了方程的良好性，并证明了解决方案的几种特性：单调性，Lipschitzness和通过变异公式表示。
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.
