Volume 8, Issue 1, February 2001, Pages 8 - 30
Correctors for Some Nonlinear Monotone Operators
Received 3 March 2000, Revised 5 June 2000, Accepted 28 August 2000, Available Online 1 February 2001.
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- 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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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 -