Fractional Sobolev-Poincar Inequalities in Irregular Domains

【Author】

Chang-Yu GUO;Department of Mathematics and Statistics, University of Jyvskyl;Department of Mathematics, University of Fribourg;

【Institution】

Department of Mathematics and Statistics, University of Jyvskyl;Department of Mathematics, University of Fribourg;

【Abstract】

This paper is devoted to the study of fractional(q, p)-Sobolev-Poincar′e inequalities in irregular domains. In particular, the author establishes(essentially) sharp fractional(q, p)-Sobolev-Poincar′e inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for the usual derivatives. Furthermore, the author verifies that those domains which support the fractional(q, p)-Sobolev-Poincar′e inequalities together with a separation property are s-diam John domains for certain s, depending only on the associated data. An inaccurate statement in [Buckley, S. and Koskela, P.,Sobolev-Poincar′e implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out.

【Keywords】

Fractional Sobolev-Poincar inequality;;s-John domain;;Quasihyperbolic boundary condition

References

To explore the background and basis of the node document

Springer Journals Database

Total: 15 articles

  • [1] F. W. Gehring;;B. P. Palka, Quasiconformally homogeneous domains, Journal d’Analyse Mathématique, 1976 (1)
  • [2] F. W. Gehring;;B. G. Osgood, Uniform domains and the quasi-hyperbolic metric, Journal d’Analyse Mathématique, 1979 (1)
  • [3] Chang-Yu Guo;;Pekka Koskela, Generalized John disks, Central European Journal of Mathematics, 2014 (2)
  • [4] Tero Kilpel?inen;;Jan Maly, Sobolev Inequalities on Sets with Irregular Boundaries, Zeitschrift für Analysis und ihre Anwendungen, 2000 (2)

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