On the Regularity of Solutions to an Adjoint Elliptic Equation with Partially VMO Coefficients

We establish, in dimension two, a regularity result for nonnegative solutions to an adjoint elliptic equation, generalizing a previous result of Escauriaza (1994). We consider elliptic equations with coefficients (1,2) which are measurable with respect to one variable and VMO with respect to the other.