Uniqueness of diffusion on domains with rough boundaries
Let Ω be a domain in Rd and h(φ)=(Formula presented.)(∂kφ,ckl∂lφ) a quadratic form on L2(Ω) with domain Cc ∞(Ω) where the ckl are real symmetric L∞(Ω)-functions with C(x)=(ckl(x)) > 0 for almost all x ∈ Ω. Further assume there are a,δ > 0 such that a-1dF δ I ≤ C ≤ a dF δ I for dF ≤ 1 where dF is the Euclidean distance to the boundary F of Ω. We assume that F is Ahlfors s-regular and if s, the Hausdorff dimension of F, is larger or equal to d - 1 we also assume a mild uniformity property for Ω...[Show more]
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