A Finite Element Approach to H1 Extension Using Prefractals
نویسنده
چکیده
We construct a linear extension operator, Π, which extends a function u in the energy domain of the fractal Koch curve S to a larger domain Ω ⊆ R. The operator Π is the limit of a sequence of operators Πn and satisfies the estimate ∥Πu∥H1(Ω) ≤ C √ E[u] + ∥u∥2L2(S,μ) where C is a numerical constant independent of u. Our approach is different and more constructive than the standard approach and exploits both the self-similarity of the fractal as well as the iterative process used to define the fractal set. ————————————————————Communicated by U. Mosco; Received August 31, 2012. This research was partially supported by NSF grant DMS-0807840. AMS Subject Classification 28A80, 46A22, 46E35
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