Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies
By Alessio Figalli, N. Fusco, Francesco Maggi, V. Millot, Massimiliano Morini. Communications in Mathematical Physics, 2014
238 citations recorded by the source corpus.
We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform with respect to s bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal s-perimeter plus a non-local repulsive interaction term. In the particular case s = 1, the s-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov (Comm. Pure Appl. Math. 66(7):1129–1162, 2013; Comm. Pure Appl. Math., 2014) concerning minimality of balls of small volume in isoperimetric problems with a competition between perimeter and a nonlocal potential term. More precisely, their result is extended to its maximal range of validity concerning the type of nonlocal potentials considered, and is also generalized to the case where local perimeters are replaced by their nonlocal counterparts.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/cd6bb6f6036b3ba4a07953350c06dca9a678c33a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- C. Bucur
- Enrico Valdinoci
- Alessio Figalli
- Lenka Slav'ikov'a
- Andrea Cianchi
- L. Pick
- Michael Loss
- Rupert L. Frank
In Computational Theory and Mathematics
- C. Bucur
- Alessio Figalli
- Enrico Valdinoci
- Andrea Cianchi
- Jean Dolbeault
- A. Alberico
- L. Pick
- Maria J. Esteban
In Materials Chemistry
Citations in the corpus
- Nonlocal Diffusion and Applications (2015, background): “[53] and [39]) and nonlocal free boundary problems (see e.”
- Fractional Orlicz-Sobolev embeddings (2020, background): “A touch of recent contributions in this connection is furnished by [7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 41, 44, 45, 51, 52, 53, 58, 59, 61, 62, 63, 64, 65, 68, 70, 71, 77, 76, 78, 83, 86].”
- Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022, background): “In fact, stability has attracted a lot of attention in recent years and we refer to [44, 26, 39, 27, 23, 30, 21, 24, 38, 25, 61, 42, 43, 40, 10] and the references within for a list of works in this direction.”