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Elliptic Boundary-Value Problems in the Sense of Lawruk on Sobolev and Hörmander Spaces

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Ukrainian Mathematical Journal Aims and scope

We study elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to a problem of this kind is bounded and Fredholm in appropriate couples of the inner product isotropic Hörmander spaces H s,φ, which form the refined Sobolev scale. The order of differentiation for these spaces is given by a real number s and a positive function φ slowly varying at infinity in Karamata’s sense. We consider this problem for an arbitrary elliptic equation Au = f in a bounded Euclidean domain Ω under the condition that u ϵ H s,φ (Ω), s < ord A, and f ϵ L 2 (Ω). We prove theorems on the a priori estimate and regularity of the generalized solutions to this problem.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    A. A. Murach & I. S. Chepurukhina

  2. Chernihiv National Pedagogical University, Chernihiv, Ukraine

    A. A. Murach

Authors
  1. A. A. Murach
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  2. I. S. Chepurukhina
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 5, pp. 672–691, May, 2015.

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Murach, A.A., Chepurukhina, I.S. Elliptic Boundary-Value Problems in the Sense of Lawruk on Sobolev and Hörmander Spaces. Ukr Math J 67, 764–784 (2015). https://doi.org/10.1007/s11253-015-1113-1

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  • DOI: https://doi.org/10.1007/s11253-015-1113-1

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