Doh, Hyun Soo2012-12-212012-12-212012-08https://hdl.handle.net/11299/141670University of Minnesota Ph.D. dissertatation. August 2012. Major:Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 60 pages.We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the approximate solutions and their difference quotients in the sup norm.en-USFinite difference approximationslp error estimatesThesis or Dissertation