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In the book Tilings and Patterns by B. Grunbaum and G. S. Shep-hard, the problem of classifying the uniform edge-c-colorings of Archimedean tilings of the Euclidean plane is posed. This article provides such a classification. A plane tiling T is a countable family of closed topological disks T = {T 1 , T 2 , ...} that cover the Euclidean plane E 2 without… (More)

- A. Cangiani, J. Chapman, E. Georgoulis, M. Jensen
- 2010

We study the advection-diffusion equation −ε∆u + b · ∇u = f in Ω ⊂ R d (1a) u = 0 on ∂Ω (1b) in a polygonal domain Ω with ε ∈ R + , b ∈ W ∞ (div, Ω) and f ∈ L 2 (Ω) where we define W ∞ (div, Ω) := {v ∈ [L ∞ (Ω)] d ; (∇ · v) ∈ L ∞ (Ω)}. It is a standard result that (1) has a unique solution in H 1 0 (Ω) provided that − 1 2 ∇ · b ≥ 0. The first term in (1a)… (More)

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