INVERSION OF CERTAIN ELLIPTIC-OPERATORS W ITH VARIABLE-COEFFICIENTS

We consider elliptic operators in divergence form with variable coeffi cients defined through an accretive sesquilinear form on the whole spa ce. The coefficients of leading order are supposed to be lipschitzian. We show how wavelets bases allow us to explicitly compute the inverse of such operators. The brat main ingredient is a detailed study, of i ndependant interest, of the convergence of the usual Galerkin approxim ations. The second main ingredient is the notion of paraproduct, suita bly adapted to our context.