Optimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set, II: Non-Convex Domains and Higher Dimensions

@article{Krejik2016OptimisationOT,
  title={Optimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set, II: Non-Convex Domains and Higher Dimensions},
  author={David Krej{\vc}iř{\'i}k and Vladimir Lotoreichik},
  journal={Potential Analysis},
  year={2016},
  volume={52},
  pages={601-614}
}
  • David Krejčiřík, Vladimir Lotoreichik
  • Published 2016
  • Mathematics, Physics
  • Potential Analysis
  • We consider the problem of geometric optimisation of the lowest eigenvalue of the Laplacian in the exterior of a compact set in any dimension, subject to attractive Robin boundary conditions. As an improvement upon our previous work (Krejčiřík and Lotoreichik J. Convex Anal. 25 , 319–337, 2018 ), we show that under either a constraint of fixed perimeter or area, the maximiser within the class of exteriors of simply connected planar sets is always the exterior of a disk, without the need of… CONTINUE READING

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