Observability estimate for the parabolic equations with inverse square potential

Abstract

<abstract><p>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 ^{[<xref ref-type="bibr" rid="b7">7</xref>]} and the Lebeau-Robbiano strategy.</p></abstract>