Observability estimate for the parabolic equations with inverse square potential
This paper investigates an observability estimate for the parabolic equations with inverse square potential in a $ C^2 $ bounded domain $ \Omega\subset\mathbb{R}^d $, which contains $ 0 $. The observation region is a product set of a subset $ E\subset(0, T] $ with positive measure and a non-empty op...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-09-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021785?viewType=HTML |
| Summary: | This paper investigates an observability estimate for the parabolic equations with inverse square potential in a $ C^2 $ bounded domain $ \Omega\subset\mathbb{R}^d $, which contains $ 0 $. The observation region is a product set of a subset $ E\subset(0, T] $ with positive measure and a non-empty open subset $ \omega\subset\Omega $ with $ 0\notin\omega $. We build up this estimate by a delicate result in measure theory in <sup>[<xref ref-type="bibr" rid="b7">7</xref>]</sup> and the Lebeau-Robbiano strategy. |
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| ISSN: | 2473-6988 |