Journal of Nonlinear Mathematical Physics

Volume 8, Issue 1, February 2001, Pages 8 - 30

Correctors for Some Nonlinear Monotone Operators

Authors
Johan Byström
Corresponding Author
Johan Byström
Received 3 March 2000, Revised 5 June 2000, Accepted 28 August 2000, Available Online 1 February 2001.
DOI
https://doi.org/10.2991/jnmp.2001.8.1.2How to use a DOI?
Abstract
In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. Here the sequence (h) tends to 0 as h and the map a (x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions. We prove that uh u weakly in W1,p 0 () as h , where u is the solution of a homogenized problem of the form -div (b (x, Du)) = f on . We also derive an explicit expression for the homogenized operator b and prove some corrector results, i.e. we find (Ph) such that Duh - Ph (Du) 0 in Lp (, Rn ).
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
8 - 1
Pages
8 - 30
Publication Date
2001/02/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2001.8.1.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Johan Byström
PY  - 2001
DA  - 2001/02/01
TI  - Correctors for Some Nonlinear Monotone Operators
JO  - Journal of Nonlinear Mathematical Physics
SP  - 8
EP  - 30
VL  - 8
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2001.8.1.2
DO  - https://doi.org/10.2991/jnmp.2001.8.1.2
ID  - Byström2001
ER  -