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Harmonic measures of perforated domains. (English) Zbl 0893.31004

The author studies the harmonic measure of a problem with holes proving the weak* convergence to a measure H(x,·;μ) defined by the relation

u(x)= Ω g(y)H(x,dy;μ)

for every g in H 1 (Ω)C(Ω), where μ is a Borel measure not charging polar sets and u is the weak solution of the relaxed Dirichlet problem

Lu+(u-g)μ=0,u-gH 0 1 (Ω)L 2 (Ω;μ)·

31B10Integral representations of harmonic functions (higher-dimensional)
35B27Homogenization; equations in media with periodic structure (PDE)