Embeddings of Anisotropic Sobolev Spaces

  • D. E. Edmunds
  • R. M. Edmunds


During the last twenty years a great deal of effort has been put into the analysis of embeddings of Sobolev spaces from the standpoint of approximation and entropy numbers. These numbers enable classifications of compact embedding maps to be made, and their intimate connection with eigenvalues of elliptic operators helps to explain the emphasis placed upon them by the strong group in the Soviet Union centred around Birman and Solomjak. Estimates have been obtained for the embeddings of the Sobolev space W k,p (Ω) in suitable Lebesgue spaces L q (Ω) when Ω is a bounded open subset of ℝ n , and even for certain types of unbounded sets Ω. When kp = n, estimates for these numbers are known for the compact embedding of W k,p (Ω) in particular Orlicz spaces.


Sobolev Space Orlicz Space Orlicz Function Intimate Connection Compact Embedding 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • D. E. Edmunds
    • 1
    • 2
  • R. M. Edmunds
    • 1
    • 2
  1. 1.Mathematics DivisionUniversity of SussexUK
  2. 2.Department of Pure MathematicsUniversity CollegeCardiffUK

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