Carleman estimates for singular parabolic equations with interior degeneracy and non-smooth coefficients

Abstract

We establish Carleman estimates for singular/degenerate parabolic Dirichlet problems with degeneracy and singularity occurring in the interior of the spatial domain. Our results are completely new, since this situation is not covered by previous contributions for degeneracy and singularity on the boundary. In addition, we consider non-smooth coefficients, thus preventing the use of standard calculations in this framework.

Keywords

• carleman estimates
• singular/degenerate equations
• non-smooth coefficients
• hardy–poincaréinequality
• caccioppoli inequality
• observability inequality
• null controllability
• 35q93
• 93b05
• 93b07
• 34h15
• 35a23
• 35b99