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.
University of Minnesota Ph.D. dissertatation.
August 2012. Major:Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 60 pages.
Doh, Hyun Soo.
Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces.
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