期刊论文详细信息
Kodai Mathematical Journal
Some remarks on a shape optimization problem
Francesco Della Pietra1 
[1] Università degli studi di Napoli "Federico II" Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
关键词: Eigenvalues;    Shape optimization;    Symmetrization;   
DOI  :  10.2996/kmj/1414674612
学科分类:数学(综合)
来源: Tokyo Institute of Technology, Department of Mathematics
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【 摘 要 】

References(17)Given a bounded open set Ω of Rn, n ≥ 2, and α ∈ R, let us considerμ(Ω,α) = $\min_{\substack{v\in W_{0}^{1,2}(\Omega)\\v\not\equiv 0}} \frac{\ds\int_{\Omega} |\nabla v|^{2}dx+\alpha \left|\ds\int_{\Omega}|v|v\,dx \right|}{\ds\int_{\Omega} |v|^{2}dx}$.We study some properties of μ(Ω,α) and of its minimizers, and, depending on α, we determine the sets Ωα among those of fixed measure such that μ(Ωα,α) is the smallest possible.

【 授权许可】

Unknown   

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