A Harnack inequality for solutions of difference differential equations of elliptic-parabolic type (Q1320996)

Consider the following difference-differential equations of elliptic- parabolic type \[ {u_ n - u_{n-1} \over h} = D_ \alpha \bigl( a_ n^{\alpha \beta} (x) D_ \beta u_ n \bigr), \quad (1 \leq n \leq N), \tag{*} \] with bounded and measurable coefficients. In the present paper the author derives a weak Harnack inequality for a weak solution of \((*)\) for parabolic and elliptic regime. Bounds and Hölder estimates for weak solutions of \((*)\) are also given.