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On the traces of Sobolev functions on the boundary of a cusp with a Hölder singularity

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Abstract

For the Sobolev classes W p 1 on a “zero” cusp with a Hölder singularity at the vertex, we consider the question of compactness of the embedding of the traces of Sobolev functions into the Lebesgue classes on the boundary of the cusp.

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References

  1. 1.

    Hajłasz P., “Sobolev spaces on an arbitrary metric space,” Potential Anal., 5, No. 4, 403–415 (1996).

  2. 2.

    Hajłasz P. and Martio O., “Traces of Sobolev functions on fractal type sets and characterization of extension domains,” J. Funct. Anal., 143, No. 1, 221–246 (1997).

  3. 3.

    Romanov A. S., “On one generalization of Sobolev spaces,” Siberian Math. J., 39, No. 4, 821–824 (1998).

  4. 4.

    Romanov A. S., “Embedding theorems for generalized Sobolev spaces,” Siberian Math. J., 40, No. 4, 787–792 (1999).

  5. 5.

    Hajłasz P. and Kinnunen J., “Hölder quasicontinuity of Sobolev functions on metric spaces,” Rev. Mat. Iberoamericana, 14, No. 3, 601–622 (1998).

  6. 6.

    Hajłasz P. and Koskela P., Sobolev met Poincaré, Amer. Math. Soc., Providence RI (2000) (Mem. Amer. Math. Soc.; 688).

  7. 7.

    Maz’ya V. G. and Poborchii S. V., “Extension of functions of S. L. Sobolev classes in the exterior of a domain with a peak vertex on the boundary. II,” Čzech. Math. J., 37, No. 1, 128–150 (1987).

  8. 8.

    Strömberg J.-O. and Torchinsky A., Weighted Hardy Spaces, Springer-Verlag, Berlin etc. (1989) (Lecture Notes in Math.; 1381).

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Original Russian Text Copyright © 2007 Romanov A. S.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 176–184, January–February, 2007.

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Romanov, A.S. On the traces of Sobolev functions on the boundary of a cusp with a Hölder singularity. Sib Math J 48, 142–149 (2007). https://doi.org/10.1007/s11202-007-0014-4

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Keywords

  • Sobolev space
  • embedding theorem
  • trace