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

Yalchin Efendiev*, Alexander Pankov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)481-492
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume6
Issue number3
DOIs
StatePublished - May 2006

Keywords

  • Elliptic
  • Finite element
  • Nonlinear

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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