The paper is about a representation formula introduced by Fusco, Moscariello, and Sbordone in [14]. The formula permits to characterize the gradient norm of a Sobolev function, defined on the whole space [Formula presented], as the limit of non-local energies (BMO-type seminorms) defined on tessellations of [Formula presented] generated by cubic cells with arbitrary orientation. We improve the main result in [14] in three different regards: we give a new concise proof of the representation formula, we analyze the case of a generic open subset [Formula presented], and consider general tessellations of Ω by means of cells more general than cubes, again arbitrarily-oriented, inspired by the creative mind of the graphic artist M.C. Escher.
BMO-type seminorms from Escher-type tessellations / Di Fratta, G.; Fiorenza, A.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 279:3(2020), p. 108556. [10.1016/j.jfa.2020.108556]
BMO-type seminorms from Escher-type tessellations
Di Fratta G.;Fiorenza A.
2020
Abstract
The paper is about a representation formula introduced by Fusco, Moscariello, and Sbordone in [14]. The formula permits to characterize the gradient norm of a Sobolev function, defined on the whole space [Formula presented], as the limit of non-local energies (BMO-type seminorms) defined on tessellations of [Formula presented] generated by cubic cells with arbitrary orientation. We improve the main result in [14] in three different regards: we give a new concise proof of the representation formula, we analyze the case of a generic open subset [Formula presented], and consider general tessellations of Ω by means of cells more general than cubes, again arbitrarily-oriented, inspired by the creative mind of the graphic artist M.C. Escher.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
