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G. Di Fratta, A. Fiorenza:
"BMO-type seminorms form Escher-type tessellations";
in: "ASC Report 17/2019", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, 1 - 19.

The paper is about a representation formula introduced by Fusco, Moscariello, and Sbordone in [ESAIM: COCV, 24(2):835--847, 2018]. The formula permits to characterize the gradient norm of a Sobolev function, defined on the whole space $\RR^n$, as the limit of non-local energies (BMO-type seminorms) defined on tessellations of $\RR^n$ generated by cubic cells. We extend the main result in [ESAIM: COCV, 24(2):835--847, 2018] in two different regards: we analyze the case of a generic open subset $\Omega\subseteq \RR^n$ and consider tessellations of $\Omega$ inspired by the creative mind of the graphic artist M.C.~Escher.

BMO-type spaces, Sobolev spaces, tessellations, tilings, cells, M.C. Escher

http://www.asc.tuwien.ac.at/preprint/2019/asc17x2019.pdf