The H\"{o}lder 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 H\"older 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 H\"{o}lder regularity of the solution when the coefficients is H\"{o}lder continuous. Moreover, the degree of H\"{o}lder regularity of the solution can be improved if the coefficient has a greater degree of H\"{o}lder regularity.