The Hölder regularity of div-curl system with anisotropic coefficients

Abstract

This research examines the regularity of weak solutions to the Div-Curl system with low regularity anisotropic coefficients. The Hölder regularity of the Div-Curl system with one anisotropic coefficient was an unresolved problem raised by Yin in 2016. We have addressed the open problem, and the findings extend to the scenario involving two anisotropic coefficients. We establish the Hölder regularity of the solution when the coefficients is Hölder continuous. Moreover, the degree of Hölder regularity of the solution can be improved if the coefficient has a greater degree of Hölder regularity.

After submitting the manuscript, we re-examined our data and discovered a significant error in our methodology which fundamentally affects the results and conclusions. We believe it would be irresponsible to proceed with the publication of these flawed findings