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

Abstract

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 𝑎𝑖𝑗(𝑥1,𝑥2) which are measurable with respect to one variable and VMO with respect to the other.