Variational Problems with Long-Range Interaction

被引：4
|
作者：
Soave, Nicola [1 ]
Tavares, Hugo [2 ,3 ]
Terracini, Susanna [4 ]
Zilio, Alessandro [5 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, Via Edoardo Bonardi 9, I-20133 Milan, Italy
[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, CAMGSD, Ave Rovisco Pais, P-1049001 Lisbon, Portugal
[3] Univ Lisbon, Dept Matemat, Fac Ciencias, Edificio C6,Piso 1, P-1749016 Lisbon, Portugal
[4] Univ Torino, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy
[5] Univ Paris Diderot Paris 7, Lab JL Lions, CNRS, UMR 7598, 8 Pl Aurelie Nemours, F-75205 Paris 13, France
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2018年 / 228卷 / 03期
基金：
欧洲研究理事会;
关键词：
OPTIMAL PARTITION PROBLEMS; STRONGLY COMPETING SYSTEMS; UNIFORM HOLDER BOUNDS; ELLIPTIC-SYSTEMS; FRACTIONAL DIFFUSION; SPATIAL SEGREGATION; FREE-BOUNDARIES; EIGENVALUES; REGULARITY; EQUATIONS;
D O I：
10.1007/s00205-017-1204-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a class of variational problems for densities that repel each other at a distance. Typical examples are given by the Dirichlet functional and the Rayleigh functional partial derivative{u(i) >0}, {u(j) > 0}) >= 1 for all(i) not equal j..minimized in the class of functions attaining some boundary conditions on a,Omega, and subjected to the constraint For these problems, we investigate the optimal regularity of the solutions, prove a free-boundary condition, and derive some preliminary results characterizing the free boundary partial derivative{Sigma(k)(i=1) u(i) > 0}.
引用
收藏
页码：743 / 772
页数：30
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