Calculus of Variations and Geometric Measure Theory

G. Di Fratta - A. Fiorenza

BMO-type seminorms from Escher-type tessellations

created by difratta on 09 Jul 2019
modified on 30 Apr 2021


Published Paper

Inserted: 9 jul 2019
Last Updated: 30 apr 2021

Journal: Journal of Functional Analysis
Volume: 279
Number: 3
Year: 2020


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 $\mathbb{R}^n$, as the limit of non-local energies (BMO-type seminorms) defined on tessellations of $\mathbb{R}^n$ 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 $\Omega\subseteq \mathbb{R}^n$ and consider tessellations of $\Omega$ inspired by the creative mind of the graphic artist M.C.~Escher.

Keywords: Sobolev spaces, BMO-type spaces, tilings, M.C. Escher