论文标题
汉密尔顿 - 雅各比在具有同源术语的度量空间中
Hamilton-Jacobi in metric spaces with a homological term
论文作者
论文摘要
几位作者已经研究了公制空间上的汉密尔顿 - 雅各比方程。遵循Gangbo和Swiech的方法，我们表明，即使我们为哈密顿式添加了同源术语，Hamilton-Jacobi方程的最终值问题也具有独特的解决方案。 在满足$ rcd（k，\ infty）$条件的度量度量空间中。特别是，可以制定粘性的汉密尔顿 - 雅各比方程。我们表明，如果同源术语足够规律，则粘性的汉密尔顿 - 雅各比方程在这种情况下也具有独特的解决方案。
The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilton-Jacobi equation has a unique solution even if we add a homological term to the Hamiltonian. In metric measure spaces which satisfy the $RCD(K,\infty)$ condition one can define a Laplacian which shares many properties with the ordinary Laplacian on $\R^n$; in particular, it is possible to formulate a viscous Hamilton-Jacobi equation. We show that, if the homological term is sufficiently regular, the viscous Hamilton-Jacobi equation has a unique solution also in this case.
