We study a linear system of pseudodifferential equations uniformly elliptic in Petrovskii’s sense in the Hilbert scale of Hörmander functional spaces defined in ℝ n . An a priori estimate is proved for the solution of the system and its interior smoothness in this scale of spaces is investigated. As an application, we establish a sufficient condition for the existence of continuous bounded derivatives of the solution.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 3, pp. 391–399, March, 2009.
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Murach, A.A. On elliptic systems in Hörmander spaces. Ukr Math J 61, 467–477 (2009). https://doi.org/10.1007/s11253-009-0215-z
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DOI: https://doi.org/10.1007/s11253-009-0215-z