Carleman 估计及其在确定性与随机偏微分方程中的应用综述

Key Points

• This work aims to review the theoretical advancements and applications of Carleman estimates in both deterministic and stochastic partial differential equations.
• Reviewed theoretical foundations of Carleman estimates and their necessary conditions.
• Derived classical Carleman estimates using second-order partial differential operators.
• Discussed key applications of Carleman estimates in unique extension, controllability, and inverse problems.
• Highlighted significant developments in Carleman estimates for unique extension and controllability.
• Outlined applications in inverse problems and their implications in recent advancements.
• Presented advancements in the application of Carleman estimates to stochastic partial differential equations.