论文标题
汉密尔顿 - 雅各比方程解决方案的收敛，具体取决于未知功能
Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function
论文作者
论文摘要
在消失的接触问题的激励中，我们在本文中研究了汉密尔顿 - 雅各比方程解决方案的收敛，具体取决于未知功能。令$ h（x，p，u）$是一种连续的哈密顿量，严格增加了$ u $，并且是$ p $的凸和强制。对于每个参数$λ> 0 $，我们用$ u^λ$表示H-J方程的唯一粘度解决方案\ [H（x，x，du（x），λu（x），λu（x））= c。\]在相当一般的假设下，我们证明$ u^λ$均匀地收集到特定的$λ$，因为$λ$ tem $λ$ ty tem tem to tem tem tem to $λ$ tem tem temiate $ n--特定的h--- h（x，du（x），0）= c。$我们还根据PEIERLS屏障和MATHER措施来表征极限解决方案。
Motivated by the vanishing contact problem, we study in the present paper the convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function. Let $H(x,p,u)$ be a continuous Hamiltonian which is strictly increasing in $u$, and is convex and coercive in $p$. For each parameter $λ>0$, we denote by $u^λ$ the unique viscosity solution of the H-J equation \[H( x,Du(x),λu(x) )=c.\] Under quite general assumptions, we prove that $u^λ$ converges uniformly, as $λ$ tends to zero, to a specific solution of the critical H-J equation $ H(x,Du(x),0)=c.$ We also characterize the limit solution in terms of Peierls barrier and Mather measures.
