Interior degenerate/singular parabolic equations in nondivergence form: well-posedness and Carleman estimates

TL;DR

This paper investigates the well-posedness and establishes Carleman estimates for interior degenerate and singular parabolic equations in nondivergence form, addressing challenges posed by interior degeneracy and singularity.

Contribution

It provides new results on well-posedness and Carleman estimates for a class of interior degenerate/singular parabolic equations in nondivergence form.

Findings

Proved well-posedness of degenerate/singular parabolic equations in nondivergence form.

Derived Carleman estimates for the associated adjoint problems.

Addressed interior degeneracy and singularity in the analysis.

Abstract

We consider non smooth general degenerate/singular parabolic equations in non divergence form with degeneracy and singularity occurring in the interior of the spatial domain, in presence of Dirichlet or Neumann boundary conditions. In particular, we consider well posedness of the problem and then we prove Carleman estimates for the associated adjoint problem.