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Non-linear eigenvalue problems for p-Laplacian with variable domain

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Abstract

In this work we consider some eigenvalue problems for p-Laplacian with variable domain. Eigenvalues of this operator are taken as a functional of the domain. We calculate the first variation of this functional, using the obtained formula investigate behavior of the eigenvalues when the domain varies. Then we consider one shape optimization problem for the first eigenvalue, prove the necessary condition of optimality relatively domain, offer an algorithm for the numerical solution of this problem.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

    Yusif S. Gasimov & Agaddin A. Niftiyev

  2. Laboratoire de Mathematiques Jean Leray, Universite de Nantes, Nantes, France

    Abdeljalil Nachaoui

Authors
  1. Yusif S. Gasimov
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  2. Abdeljalil Nachaoui
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  3. Agaddin A. Niftiyev
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Correspondence to Yusif S. Gasimov.

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Gasimov, Y.S., Nachaoui, A. & Niftiyev, A.A. Non-linear eigenvalue problems for p-Laplacian with variable domain. Optim Lett 4, 67–84 (2010). https://doi.org/10.1007/s11590-009-0143-8

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  • DOI: https://doi.org/10.1007/s11590-009-0143-8

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