The paper considers a differential equation, which is given by a non-self-adjoint, closed and reversible second order operator in the Lebesgue space . It is assumed that the variable coefficients  on the derivatives  are non-degenerate and can change sign in any neighborhood of . As a result, we obtain a coercive estimate for solutions of this equation in terms of point multipliers on a pair of weighted Sobolev spaces . The weight functions in these spaces are directly related to the variable coefficients of the equation under consideration. A point multiplier on a pair of function spaces  is a function that defines a bounded multiplication operator  from  to . The essence of coercive estimates is that they give functional characteristics for solutions, such as, for example, smoothness, summability, etc. The method of local estimates on intervals of special length was used to solve the problem. This method makes it possible to reveal a number of characteristics that are important in the theory of differential operators, relying on internal connections of variable coefficients, rather than setting them a priori.