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Essential spectrum of elliptic systems of pseudo-differential operators on \(L^2({{\mathbb {R}}}^N) \oplus L^2({{\mathbb {R}}}^N)\)

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Abstract

Inspired by a result of Wong (Partial Differ Equ 13(10):1209–1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on \(L^2({{\mathbb {R}}}^N) \oplus L^2({{\mathbb {R}}}^N)\) that are uniformly Douglis–Nirenberg elliptic with positive-order diagonal entries. We apply our result to a problem arising in the dynamics of falling liquid films.

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Acknowledgements

The authors gratefully acknowledge the support of the Swiss National Science Foundation, SNF Grant No. \(200020\_146477\). The first author also gratefully acknowledges the support of SNF Early Postdoc.Mobility Grant No. 168723 and thanks the Department of Mathematics at University College London for the kind hospitality.

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  1. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK

    Orif O. Ibrogimov

  2. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Christiane Tretter

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  1. Orif O. Ibrogimov
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  2. Christiane Tretter
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Correspondence to Christiane Tretter.

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Ibrogimov, O.O., Tretter, C. Essential spectrum of elliptic systems of pseudo-differential operators on \(L^2({{\mathbb {R}}}^N) \oplus L^2({{\mathbb {R}}}^N)\) . J. Pseudo-Differ. Oper. Appl. 8, 147–166 (2017). https://doi.org/10.1007/s11868-017-0198-8

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  • DOI: https://doi.org/10.1007/s11868-017-0198-8

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