Some Homogenization and Corrector Results for Nonlinear Monotone Operators

DOI

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 ).

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Peter Wall
PY  - 1998
DA  - 1998/08/01
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  - 10.2991/jnmp.1998.5.3.7
ID  - Wall1998
ER  -