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In this paper, we investigate a class of $n$-dimensional degenerate parabolicequations with abstract coefficients. Our focus is on improving the regularityof solutions and establishing Carleman estimates for these equations throughthe construction of specialized weight functions. Using these results, wedemonstrate the null controllability of the corresponding equations.Additionally, we provide a specific example to illustrate the efficacy of ourmethodology.

Null controllability of a kind of n-dimensional degenerate parabolic equation