带粗糙系数和界面的波动方程与板方程的可观测性：乘子方法
Observability of wave and plate equations with rough coefficients and interfaces: a multiplier approach
AI总结：
本文采用乘子方法，通过正则化过程推导主部含粗糙系数及界面的波动方程与板方程的可观测性，避免分析奇异集合附近解的正则性，建立了含界面情形的新可观测性结果。
AI中文摘要：
本文旨在通过正则化过程推导主部含粗糙系数（包括界面情形）的波动方程与板方程的可观测性性质。具体而言，我们证明：若奇异系数可由对应一致可观测系统的光滑系数序列逼近，则可观测性不等式可传递至极限，从而得到极限系统的可观测性性质。该策略虽自然，但我们证明其可用于建立若干情形下的新可观测性结果，特别是在界面与边界相遇或多个界面交于一点的情形，此时需满足乘子型条件，对界面处系数的跳跃施加符号约束。该方法的关键优势在于，无需对系数奇异集合附近解的正则性进行详细分析。
英文摘要：
The goal of this article is to derive observability properties for wave and plate equations with rough coefficients in the principal part, including the case of interfaces, through a regularization process. Specifically, we demonstrate that if a singular coefficient can be approximated by a sequence of smooth coefficients corresponding to uniformly observable systems, then the observability inequalities can be passed to the limit. This allows us to derive observability properties for the limit system. While this strategy is natural, we show that it can be used to establish new observability results in several settings, particularly in the presence of interfaces meeting the boundary, or multiple interfaces intersecting at a point, under a suitable multiplier-type condition that imposes sign constraints on the jumps of the coefficients at the interfaces. A key advantage of this approach is that it avoids the need for a detailed analysis of the regularity of solutions near the sets where the coefficients are singular.
