Corpus ID: 210116850

Shape optimization of a weighted two-phase Dirichlet eigenvalue

  title={Shape optimization of a weighted two-phase Dirichlet eigenvalue},
  author={Idriss Mazari and Gr'egoire Nadin and Yannick Privat},
  • Idriss Mazari, Gr'egoire Nadin, Yannick Privat
  • Published 2020
  • Mathematics
  • Let $m$ be a bounded function and $\alpha$ a nonnegative parameter. This article is concerned with the first eigenvalue $\lambda_\alpha(m)$ of the drifted Laplacian type operator $\mathcal L_m$ given by $\mathcal L_m(u)= -\operatorname{div} \left((1+\alpha m)\nabla u\right)-mu$ on a smooth bounded domain, with Dirichlet boundary conditions. Assuming uniform pointwise and integral bounds on $m$, we investigate the issue of minimizing $\lambda_\alpha(m)$ with respect to $m$. Such a problem is… CONTINUE READING

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