Existence and Regularity of Minimizers for Some Spectral Functionals with Perimeter Constraint

被引：34
|
作者：
De Philippis, Guido [1 ]
Velichkov, Bozhidar [2 ]
机构：
[1] Hausdorff Ctr Math, D-53115 Bonn, Germany
[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2014年 / 69卷 / 02期
关键词：
Shape optimization; Eigenvalues; Free boundary; Concentration-compactness; SHAPE OPTIMIZATION; DIRICHLET PROBLEMS; MINIMIZATION; EIGENVALUE; LAPLACIAN;
D O I：
10.1007/s00245-013-9222-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we prove that the shape optimization problem min {lambda(k)(Omega) : Omega subset of R-d, Omega open, P(Omega) = 1, vertical bar Omega vertical bar < +infinity} has a solution for any and dimension d. Moreover, every solution is a bounded connected open set with boundary which is C (1,alpha) outside a closed set of Hausdorff dimension d-8. Our results are more general and apply to spectral functionals of the form f(lambda(k)(Omega), ... ,lambda(kp)(Omega)) for increasing functions f satisfying some suitable bi-Lipschitz type condition.
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页码：199 / 231
页数：33
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