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Parametric Dependence of Boundary Trace Inequalities

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Differential and Difference Equations with Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

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Abstract

Some results about the dependence of the optimal constants in some trace inequalities for H 1-functions on a region \(\Omega \) are described. These constants are shown to be the primary Steklov eigenvalue of \(\mu I - \Delta \) on the region. They are related to the norm of an associated trace operator. In particular the eigenvalue is shown to be a locally Lipschitz continuous function of μ, and its inverse is a convex function of μ.

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References

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Acknowledgements

This research was partially supported by NSF awards DMS 0808115 and 1108754.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204-3008, USA

    Giles Auchmuty

Authors
  1. Giles Auchmuty
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Correspondence to Giles Auchmuty .

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Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Auchmuty, G. (2013). Parametric Dependence of Boundary Trace Inequalities. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_18

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