Correctors for Some Nonlinear Monotone Operators

DOI

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 ).

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  - 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  - 10.2991/jnmp.2001.8.1.2
ID  - Byström2001
ER  -