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Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues

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 نشر من قبل Alfred Wagner
 تاريخ النشر 2015
  مجال البحث
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The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental frequency, are derived. The main question is whether or not the classical isoperimetric inequalities for the fundamental frequency of membranes hold in this case. The arguments are based on the harmonic transplantation for the global results and the shape derivatives (domain variations) for nearly circular domain.



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