Harnack's Inequality and Applications of Quasilinear Degenerate Elliptic Equations with Rough and Singular Coefficients

摘要

We consider the quasilinear degenerate elliptic equation with rough and singular coefficients of the form in an open set where the quadratic form associated with the principle part of this equation allows vanishing and the coefficients in structural conditions on and require no smoothness but belong to some Stummel-Kato class. We prove a Fefferman-Phong type inequality related to the Stummel-Kato class and then an embedding inequality. Based on these inequalities, the local boundedness and Harnack's inequality of the weak solutions are derived. As applications, the continuity and Holder continuity for the nonnegative weak solutions are given.