Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies
Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies
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DOI：
10.1007/s00220-014-2244-1
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发表时间：
2014-03
影响因子：
2.4
通讯作者：
A. Figalli;N. Fusco;F. Maggi;V. Millot;M. Morini
中科院分区：
文献类型：
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作者：
A. Figalli;N. Fusco;F. Maggi;V. Millot;M. Morini
我们得到了一个尖锐的定量等周不等式的非局部周长，一致的关于有界远离0。这使我们能够解决球的局部和全局极小性质相对于体积约束的自由能最小化组成的非本地周长加上非本地排斥相互作用项。在= 1的特殊情况下，这些周长与经典周长一致，并且我们的结果改进了Knuepfer和Muratov的结果（Comm. Pure Appl. Math. 66（7）：1129-1162，2013; Comm. Pure Appl. Math.，2014）关于等周问题中小体积球的极小性，周长和非局部势项之间存在竞争。更确切地说，他们的结果是延长到其最大范围的有效性有关的类型的非局部潜力考虑，也推广到当地的周长被取代的情况下，他们的非本地同行。
We obtain a sharp quantitative isoperimetric inequality for nonlocals-perimeters, uniform with respect tosbounded 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 nonlocals-perimeter plus a non-local repulsive interaction term. In the particular cases= 1, thes-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.