Observability estimate for the parabolic equations with inverse square potential

Abstract

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 [7] and the Lebeau-Robbiano strategy.

Keywords

• observability estimate
• parabolic equations
• spectral inequality
• inverse square potential