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

Orif O. Ibrogimov; Christiane Tretter

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arXiv · 1703.06344

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

Orif O. Ibrogimov·Christiane Tretter

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Abstract

Inspired by a result of Wong (Commun. 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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BibTeX RIS

Orif O. Ibrogimov, Christiane Tretter. 2017-03-18. Essential spectrum of elliptic systems of pseudo-differential operators on $L^2(\mathbb{R}^N)\oplus L^2(\mathbb{R}^N)$. https://arxiv.org/abs/1703.06344

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