Douglis–Nirenberg systems uniformly elliptic in ℝn are studied in the class of Hörmander Hilbert spaces Hφ; where φ is an RO-varying function of scalar argument. An a priori estimate is established for the solutions, and their interior regularity is investigated. A sufficient condition under which these systems possess the Fredholm property is obtained.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 11, pp. 1477–1491, November, 2012.
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Zinchenko, T.N., Murach, A.A. Douglis–Nirenberg elliptic systems in Hörmander spaces. Ukr Math J 64, 1672–1687 (2013). https://doi.org/10.1007/s11253-013-0743-4
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DOI: https://doi.org/10.1007/s11253-013-0743-4