AI 中文总结
研究\(\mathbb{R}^N\)中有界利普希茨区域\(\Omega\)上\(p -\)拉普拉斯算子第一罗宾特征值在\(\beta\)趋于\(0\)和\(+\infty\)时的渐近行为，推导精确渐近展开式，在特定假设下得到狄利克雷极限展开式。
AI 中文摘要
设\(\Omega\)是\(\mathbb{R}^N\)（\(N\geq2\)）中的有界利普希茨区域。本文研究\(p -\)拉普拉斯算子的第一罗宾特征值在\(\beta\)趋于\(0\)和趋于\(+\infty\)时的渐近行为，推导特征值的精确渐近展开式；在\(\partial\Omega\)为\(C^{1,1}\)类的额外假设下得到狄利克雷极限\(\beta\to+\infty\)时的展开式。
英文摘要
Let $Ω$ be a bounded Lipschitz domain of $\mathbb R^N$, $N\geq 2$. In this paper, we study the asymptotic behavior of the first Robin eigenvalue of the $p$-Laplace operator as $β$ goes to $0$ and as $β$ goes to $+\infty$, deriving sharp asymptotic expansions of the eigenvalue; the expansion in the Dirichlet limit $β\to+\infty$ is obtained under the additional assumption that $\partialΩ$ is of class $C^{1,1}$.
