Carleman estimates for degenerate parabolic equations with first order terms and applications

In this Note we prove a Carleman estimate for the one-dimensional degenerate parabolic equation v t + ( x α v x ) x − b ( x , t ) v + ( x β / 2 c ( x , t ) v ) x = 0 , ( x , t ) ∈ ( 0 , 1 ) × ( 0 , T ) , where α ∈ [ 0 , 2 ) , β ⩾ α and b ( x , t ) , c ( x , t ) ∈ L ∞ ( ( 0 , 1 ) × ( 0 , T ) ) and give some controllability consequences.