A sharp relative isoperimetric inequality for the square

Haim Brezis; Alfred Bruckstein

doi:10.5802/crmath.243

Équations aux dérivées partielles

A sharp relative isoperimetric inequality for the square

Haim Brezis ^1,^2,³ ; Alfred Bruckstein ⁴

¹ Dept. of Mathematics, Rutgers University, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA
² Depts. of Mathematics and Computer Science,Technion – IIT, Haifa 32000, Israel
³ Laboratoire J.-L. Lions, Sorbonne Universités, UPMC, Université Paris-6, 4 place Jussieu, 75005 Paris, France
⁴ Dept. of Computer Science, Technion – IIT, Haifa 32000, Israel

Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1191-1199.

Résumé

We compute the exact value of the least “relative perimeter” of a shape $S$ , with a given area, contained in a unit square; the relative perimeter of $S$ being the length of the boundary of $S$ that does not touch the border of the square.

Reçu le : 2021-07-08
Accepté le : 2021-07-08
Publié le : 2021-11-25

DOI : 10.5802/crmath.243

Affiliations des auteurs :

Haim Brezis ^{1, 2, 3} ; Alfred Bruckstein ⁴

¹ Dept. of Mathematics, Rutgers University, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA
² Depts. of Mathematics and Computer Science,Technion – IIT, Haifa 32000, Israel
³ Laboratoire J.-L. Lions, Sorbonne Universités, UPMC, Université Paris-6, 4 place Jussieu, 75005 Paris, France
⁴ Dept. of Computer Science, Technion – IIT, Haifa 32000, Israel

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Haim Brezis and Alfred Bruckstein},
     title = {A sharp relative isoperimetric inequality for the square},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1191--1199},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {9},
     year = {2021},
     doi = {10.5802/crmath.243},
     language = {en},
}

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Haim Brezis; Alfred Bruckstein. A sharp relative isoperimetric inequality for the square. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1191-1199. doi : 10.5802/crmath.243. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.243/

Bibliographie
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