抛物型方程的对数凸Carleman换位子方法
Carleman commutator approach in logarithmic convexity for parabolic equations
摘要：
本文研究有界区域上热方程的对数凸性（或频率函数）与Carleman交换子相结合的一种新策略，得到了一次观测估计.我们还考虑了具有平方反比势的热传导方程。此外，还导出了相应的本征值问题的谱不等式。
英文摘要：
In this paper we investigate on a new strategy combining the logarithmic convexity (or frequency function) and the Carleman commutator to obtain an observation estimate at one time for the heat equation in a bounded domain. We also consider the heat equation with an inverse square potential. Moreover, a spectral inequality for the associated eigenvalue problem is derived.
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