Analytic monotone extension in two and three dimensions
Let Ω denote the simplicial complex [0, 1]d in ℛd. For a nonnegative integer p with p ≤ d, let Ω(p) denote the p- skeleton of Ω Let d = 2 or 3 and suppose that f is a monotone function on Ω(1). We give construction schemes which extend f as a monotone function on Ω, while maintaining smoothness. Our results are related to those of Dahmen, DeVore and Micchelli for the case d = 2 and p = 1.
Analytic monotone extension, p-skeleton, Simplicial complex
Kilmer, Shelby, Xingping Sun, and Xiangming Yu. "Analytic monotone extension in two and three dimensions." Numerical Functional Analysis and Optimization 18, no. 1-2 (1997): 131-141.
Numerical Functional Analysis and Optimization