Partial differential equations
A sharp relative isoperimetric inequality for the square
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1191-1199.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.243
Brezis, Haim 1, 2, 3; Bruckstein, Alfred 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
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Brezis, Haim; Bruckstein, Alfred. A sharp relative isoperimetric inequality for the square. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1191-1199. doi : 10.5802/crmath.243. http://www.numdam.org/articles/10.5802/crmath.243/

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