Observability Inequalities and Measurable Sets
Observability Inequalities and Measurable Sets
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DOI：
10.4171/jems/490
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
J. Apraiz;L. Escauriaza;G. Wang;C. Zhang
中科院分区：
文献类型：
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作者：
J. Apraiz;L. Escauriaza;G. Wang;C. Zhang
给出了$Omega\times（0，T）上热方程的两个能观性不等式.在第一种情况下，观测来自$\Omega\times（0，T）$中的正测度子集，而在第二种情况下，观测来自$\partial\Omega \times（0，T）$中的正表面测度子集。证明了当$\Omega$是有界Lipschitz局部星形域时的Lebeau-Robbiano谱不等式.给出了上述能观性不等式的一些应用。
This paper presents two observability inequalities for the heat equation over $\Omega\times(0,T)$. In the first one, the observation is from a subset of positive measure in $\Omega\times(0,T)$, while in the second, the observation is from a subset of positive surface measure in $\partial\Omega \times(0,T)$. It also proves the Lebeau-Robbiano spectral inequality when $\Omega$ is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.