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Sobolev-Like Hilbert Spaces Induced by Elliptic Operators

  • Tetiana Kasirenko
  • Vladimir Mikhailets
  • Aleksandr MurachEmail author
Article
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Abstract

We investigate properties of function spaces induced by the inner product Sobolev spaces \(H^{s}(\Omega )\) over a bounded Euclidean domain \(\Omega \) and by an elliptic differential operator A on \({\overline{\Omega }}\). The domain and the coefficients of A are of the class \(C^{\infty }\). These spaces consist of all distributions \(u\in H^{s}(\Omega )\) such that \(Au\in H^{\lambda }(\Omega )\) and are endowed with the corresponding graph norm, with \(s,\lambda \in {\mathbb {R}}\). We prove an interpolation formula for these spaces and discuss their application to elliptic boundary-value problems.

Keywords

Sobolev space Elliptic operator Complex interpolation Elliptic problem Fredholm operator 

Mathematics Subject Classification

Primary 46E35 35J30 Secondary 35J40 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tetiana Kasirenko
    • 1
  • Vladimir Mikhailets
    • 1
  • Aleksandr Murach
    • 1
    Email author
  1. 1.Institute of Mathematics of National Academy of Sciences of UkraineKyivUkraine

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