On the Fractional Regularity for an Elliptic Nonlinear Singular Drift Equation

ABSTRACT We consider an elliptic equation with the fractional Laplacian operator in the dissipative term, a singular integral operator in the nonlinear term, and an external source . The key example is the stationary (time‐independent) counterpart of the surface quasi‐geostrophic equation. Under suitable assumptions on and natural assumptions on in the setting of Sobolev spaces, our main result examines how the fractional power propagates and optimally improves the regularity of weak ‐solutions to this equation.