Journal of Nonlinear Mathematical Physics

Volume 5, Issue 3, August 1998, Pages 331 - 348

Some Homogenization and Corrector Results for Nonlinear Monotone Operators

Authors
Peter WALL
Corresponding Author
Peter WALL
Available Online 1 August 1998.
DOI
https://doi.org/10.2991/jnmp.1998.5.3.7How to use a DOI?
Abstract
This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form - div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. The sequence (h) tends to 0 and the map a(x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions. It is proved that uh u weakly in H1,2 0 (), where u is the solution of a homogenized problem - div(b(x, Du)) = f on . We also prove some corrector results, i.e. we find (Ph) such that Duh - Ph(Du) 0 in L2 (, Rn ).
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
5 - 3
Pages
331 - 348
Publication Date
1998/08
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1998.5.3.7How 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  - Peter WALL
PY  - 1998
DA  - 1998/08
TI  - Some Homogenization and Corrector Results for Nonlinear Monotone Operators
JO  - Journal of Nonlinear Mathematical Physics
SP  - 331
EP  - 348
VL  - 5
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.3.7
DO  - https://doi.org/10.2991/jnmp.1998.5.3.7
ID  - WALL1998
ER  -