Fractional Sobolev-Poincaré inequalities in irregular domains
- Guo, Chang-Yu Department of Mathematics and StatisticsUniversity of Jyväskylä, Finland - Department of MathematicsUniversity of Fribourg, Switzerland
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01.05.2017
Published in:
- Chinese Annals of Mathematics, Series B. - 2017, vol. 38, no. 3, p. 839–856
English
This paper is devoted to the study of fractional (q, p)-Sobolev-Poincaré in- equalities in irregular domains. In particular, the author establishes (essentially) sharp fractional (q, p)-Sobolev-Poincaré 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-Poincaré 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-Poincaré implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 305695
- DOI 10.1007/s11401-017-1099-0
- Persistent URL
- https://folia.unifr.ch/unifr/documents/306148
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