We consider an elliptic equation with the fractional Laplacian operator (-) ^{2} in the dissipative term, a singular integral operator A () in the nonlinear term, and an external source f. The key example is the stationary (time-independent) counterpart of the surface quasi-geostrophic equation. Under suitable assumptions on f and natural assumptions on A () in the setting of Sobolev spaces, our main result examines how the fractional power propagates and optimally improves the regularity of weak Lᵖ-solutions to this equation.
Oscar Jarrín (Sat,) studied this question.