Regularity result for a shape optimization problem under perimeter constraint
作者： Beniamin Bogosel
DOI:
关键词: Bounded function 、 Laplace operator 、 Mathematical analysis 、 Perimeter 、 Constraint (information theory) 、 Dimension (vector space) 、 Dirichlet distribution 、 Eigenvalues and eigenvectors 、 Curvature 、 Mathematics
摘要: We study the problem of optimizing eigenvalues Dirichlet Laplace operator under perimeter constraint. prove that optimal sets are analytic outside a closed singular set dimension at most $d-8$ by writing general optimality condition in case eigenvalue is multiple. As consequence we find $k$-th strictly smaller than $(k+1)$-th eigenvalue. also provide an elliptic regularity result for with positive and bounded weak curvature.
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arxiv.org参考文章(13)
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