论文标题
PUCCI操作员的小扩散和短期渐近学
Small diffusion and short-time asymptotics for Pucci operators
论文作者
论文摘要
在以下两个问题的情况下，本文介绍了{\ it Pucci的极端运算符} $ \ Mathcal {m}^\ pm $的渐近公式。它被认为是$ - \ varepsilon的$ u^\ varepsilon（x）$的$ - 在这里，$ω\ subset \ mathbb {r}^n $是一个域（不一定有限），而$γ$是其边界。它也被认为$ v（x，t）$ $ v_t- \ \ mathcal {m}^\ pm \ left（\ nabla^2 v \ right）= 0 $ in $ω\ times（0，\ infty）$，$ v = 1 $ on $γ\ times in $γ\ times（0，\ infty）$和$ v = 0 $ ph = 0 $ ph = 0 $ {0，本着他们以前的作品的精神，作者将配置文件建立为$ \ varepsilon $或$ t \ to $ u^\ varepsilon（x）$和$ v（x，t）$的值，以及其$ q $ - 米恩在接触$γ$的球上的$ q $。结果代表了瓦拉达汉（Varadhan）和线性方案中的magninini-sakaguchi获得的延伸的进一步步骤。
This paper presents asymptotic formulas in the case of the following two problems for the {\it Pucci's extremal operators} $\mathcal{M}^\pm$. It is considered the solution $u^\varepsilon(x)$ of $-\varepsilon^2 \mathcal{M}^\pm\left(\nabla ^2 u^\varepsilon\right)+u^\varepsilon=0$ in $Ω$ such that $u^\varepsilon=1$ on $Γ$. Here, $Ω\subset \mathbb{R}^N$ is a domain (not necessarily bounded) and $Γ$ is its boundary. It is also considered $v(x,t)$ the solution of $v_t - \mathcal{M}^\pm\left(\nabla^2 v\right)=0$ in $Ω\times (0,\infty)$, $v=1$ on $Γ\times(0,\infty)$ and $v=0$ on $Ω\times \{0\}$. In the spirit of their previous works, the authors establish the profiles as $\varepsilon$ or $t\to 0^+$ of the values of $u^\varepsilon(x)$ and $v(x,t)$ as well as of those of their $q$-means on balls touching $Γ$. The results represent a further step in the extensions of those obtained by Varadhan and by Magnanini-Sakaguchi in the linear regime.
