Optimizing the first eigenvalue of some quasilinear operators with respect to the boundary conditions

Francesco Della Pietra; Nunzia Gavitone; Hynek Kovarik

Optimizing the first eigenvalue of some quasilinear operators with respect to the boundary conditions

Analysis of PDEs 2015-11-12 v1

Authors: Francesco Della Pietra , Nunzia Gavitone , Hynek Kovarik

Abstract

We consider a class of quasilinear operators on a bounded domain $\Omega\subset \mathbb R^n$ and address the question of optimizing the first eigenvalue with respect to the boundary conditions, which are of the Robin-type. We describe the optimizing boundary conditions and establish upper and lower bounds on the respective maximal and minimal eigenvalue.

Keywords

quasilinear operators eigenvalue optimization boundary conditions Robin boundary conditions first eigenvalue

Cite

@article{arxiv.1511.03596,
  title  = {Optimizing the first eigenvalue of some quasilinear operators with respect to the boundary conditions},
  author = {Francesco Della Pietra and Nunzia Gavitone and Hynek Kovarik},
  journal= {arXiv preprint arXiv:1511.03596},
  year   = {2015}
}

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