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

TL;DR

This paper develops novel Carleman estimates for singular and degenerate parabolic equations with interior degeneracy and non-smooth coefficients, addressing a gap in existing mathematical analysis methods.

Contribution

It introduces the first Carleman estimates for interior degeneracy and singularity in parabolic equations with non-smooth coefficients, expanding the scope of controllability and inverse problems.

Findings

Established new Carleman estimates for interior degeneracy.

Handled non-smooth coefficients in the analysis.

Provided foundational tools for control theory in complex PDEs.

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.