Carleman estimates for the heat equation with discontinuous diffusion coefficients

Abstract

We consider the heat equation with a diffusion coefficient that is discontinuous at an interface. We give global Carleman estimates for solutions of this equation, even if the jump of the coefficient across the interface has not a constant sign.

Keywords:

• heat equation
• Carleman estimates
• discontinuous coefficients

AMS subject classifications: :

• 35K05
• 35K55
• 35R05
• 35R30