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Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN: 1473-7124, Vol: 145, Issue: 1, Page: 31-45
2015
  • 23
    Citations
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  • 4
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Metrics Details

  • Citations
    23
    • Citation Indexes
      23
  • Captures
    4

Article Description

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p < 1) in a Lipschitz bounded domain Ω in R. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne-Weinberger inequality.

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