On parabolic partial differential equations with Hölder continuous diffusion coefficients

We investigate existence and regularity of weak solutions a 1-dimensional parabolic differential equation with non-constant Hölder diffusion coefficient rough forcing term. Such an appears in studying the Ericksen-Leslie model for nematic liquid crystals where our result applies. The presented here uses continuity which comes from physical background analysis model. Moreover, dependence exponent solution is explicit on coefficient.