黎曼流形上的相对法伯-克拉恩不等式与特鲁丁格方程
Relative Faber--Krahn inequalities and Trudinger's equation on Riemannian Manifolds
中文总结 AI 辅助
该研究在黎曼流形上探讨特鲁丁格方程，证明相对p-法伯-克拉恩不等式等价于体积加倍与次高斯上估计的结合，还导出了改进的长时间上估计。
中文摘要 AI 辅助
我们在黎曼流形上考虑特鲁丁格方程∂_t u = Δ_p u^(1/(p-1))，其中p>1。我们证明相对p-法伯-克拉恩不等式等价于体积加倍条件与特鲁丁格方程非负有界弱下解的次高斯上估计的结合；还在一致p-法伯-克拉恩不等式下导出了改进的长时间上估计。
英文摘要
We consider on Riemannian manifolds the Trudinger equation \begin{equation*}\partial _{t}u=Δ_{p}u^{\frac{1}{p-1}},\end{equation*} where $p>1$. We prove that a relative $p$--Faber--Krahn inequality is equivalent to the conjunction of volume doubling and a sub-Gaussian upper estimate for non-negative bounded weak subsolutions of Trudinger's equation. We also derive an improved long-time upper estimate under a uniform $p$--Faber--Krahn inequality.
