论文标题
对一阶汉密尔顿 - 雅各比方程的全球半腔，具有状态限制
Global semiconcavity of solutions to first-order Hamilton-Jacobi equations with state constraints
论文作者
论文摘要
我们专注于针对一阶汉密尔顿的全球半充电 - 具有州限制的雅各比方程，尤其是对于hamiltonian $ h（x，β）：= | = |> |β|^p-f（x）$，$ p \ in $ p \ in（1，2] $。我们首先表明该解决方案在每个局部依赖于半段的时间表，并在第一次依赖半段的时间段，并在半度性上进行了分析，并将量度用于半度性的时间段，并将其限制在半度性上，并依赖于半含量的时间段，并将其分为半循环。从这一点开始，在$ df $上的适当条件下，我们证明，对于任何最小化曲线，击中域的边界的时间为$+\ infty $，因此，该解决方案在全球范围内是$ df $的情况。 KAM理论。
We focus on the global semiconcavity of solutions to first-order Hamilton--Jacobi equations with state constraints, especially for the Hamiltonian $H(x, β):=|β|^p-f(x)$ with $p \in (1, 2]$. We first show that the solution is locally semiconcave, and the semiconcavity constant at each point depends on the first time a corresponding minimizing curve emanating from this point hits the boundary. Then, with appropriate conditions on $Df$, we prove that for any such minimizing curve, the time it takes to hit the boundary of the domain is $+\infty$, and as a consequence, the solution is globally semiconcave. Moreover, the condition on $Df$ is essentially optimal with examples in one-dimensional space. The proofs employ the Euler-Lagrange equations and techniques in weak KAM theory.
