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

Yalchin Efendiev; Alexander Pankov

doi:10.3934/dcdsb.2006.6.481

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 journal › Article › peer-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 language	English (US)
Pages (from-to)	481-492
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	6
Issue number	3
DOIs	https://doi.org/10.3934/dcdsb.2006.6.481
State	Published - May 2006
Externally published	Yes

Keywords

Elliptic
Finite element
Nonlinear

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2006.6.481

Cite this

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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.",

keywords = "Elliptic, Finite element, Nonlinear",

author = "Yalchin Efendiev and Alexander Pankov",

year = "2006",

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doi = "10.3934/dcdsb.2006.6.481",

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AU - Pankov, Alexander

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AB - 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.

KW - Elliptic

KW - Finite element

KW - Nonlinear

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DO - 10.3934/dcdsb.2006.6.481

M3 - Article

AN - SCOPUS:33745257049

SN - 1531-3492

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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