On exponent in the Hölder condition for the first order derivatives of a solution to a linear elliptic second order equation with two variables (Q376524)

This paper is concerned with interior Hölder regularity of weak solutions to second-order linear partial differential equations with measurable coefficients in dimension two. The main result establishes that the weak derivatives of \(W^{2,2}\) solutions are Hölder continuous with the exponent \(\frac{\sqrt{33}-3}{2} \frac{\nu}{\nu^2+1}\) in the interior of the domain, where \(\nu\) represents the elliptic constant of the differential operator. The sharpness of this results is illustrated by several examples.