Asymptotic behaviour of quasi-linear problems with neumann boundary conditions on perforated domains

Abstract

In this paper we deal with the limit behaviour of the solutions u_h of quasi-linear equations -div f on perforated domains with homogeneous Neumann boundary conditions on the holes. Under suitable assumptions on a_h and ω_h we prove that certain extensions of u_h converge weakly in H^1,p(ω) to the solution u of a quasi-linear equation of the form -div(a(x,Du)) = f, where the function a is independent of f and has the same qualitative properties of a_h

Keywords:

• T-convergence
• monotone operators
• Neumann boundary conditions
• perforated domains

AMS(MOS):

• 35B40
• 35J65