May  2006, 6(3): 481-492. doi: 10.3934/dcdsb.2006.6.481

Meyers type estimates for approximate solutions of nonlinear elliptic equations and their applications

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368

2. 

Department of Mathematics, College of William & Mary, Williamsburg, VA 23187-8795, United States

Received  December 2004 Revised  December 2005 Published  February 2006

In this paper we obtain Meyers type regularity estimates for approximate solutions of nonlinear elliptic equations. These estimates are used in the analysis of a numerical scheme obtained from a numerical homogenization of nonlinear elliptic equations. Numerical homogenization of nonlinear elliptic equations results in discretization schemes that require additional integrability of the approximate solutions. The latter motivates our work.
Citation: Y. Efendiev, Alexander Pankov. Meyers type estimates for approximate solutions of nonlinear elliptic equations and their applications. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 481-492. doi: 10.3934/dcdsb.2006.6.481
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