Three-spindle inequality for parabolic equations: A simplified approach to the three-cylinder inequality

Abstract We consider quantitative unique continuation estimates for solutions of second-order parabolic equations. Our approach provides a substantial simplification of the proof of the three-cylinder inequality, which is a key tool in deriving optimal stability estimates in inverse problems with a time-independent unknown boundary. The simplification is achieved by proving a Carleman estimate with a suitable singular weight, leading to what we call the three-spindle inequality which directly implies the three-cylinder inequality.