论文标题
四阶部分差分运算符和应用的统一加权不平等
A unified weighted inequality for fourth-order partial differential operators and applications
论文作者
论文摘要
在本文中，我们建立了针对第四阶部分差分操作员的基本不平等，$ \ cal p =α\ partial_s+β\ partial_ {ss}+δ^2 $（$α，β\ in \ mathbb {r} $）具有带有抽象的指定型号 - 型号 - 型号型号 - type-Type type typeptype type type type type type。这种重量功能不仅包括常规重量功能，还包括奇异的重量功能。使用这种不平等，我们能够证明对操作员$ \ cal p $的Carleman估计值在$β<0 $或$α\ neq 0，β= 0 $的情况下具有一些合适的边界条件。作为应用程序，我们获得了$ \ cal p $的分解估计，这可能意味着使用夹紧边界条件或铰链边界条件的板方程产生对数型稳定结果。
In this paper, we establish a fundamental inequality for fourth order partial differential operator $\cal P=α\partial_s+β\partial_{ss}+Δ^2$ ($α, β\in\mathbb{R}$) with an abstract exponential-type weight function. Such kind of weight functions including not only the regular weight functions but also the singular weight functions. Using this inequality we are able to prove some Carleman estimates for the operator $\cal P$ with some suitable boundary conditions in the case of $β<0$ or $α\neq 0, β=0$. As application, we obtain a resolvent estimate for $\cal P$, which can imply a log-type stabilization result for the plate equation with clamped boundary conditions or hinged boundary conditions.
