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Hardy's inequality in a limiting case on general bounded domains.
- Source :
-
Communications in Contemporary Mathematics . Dec2019, Vol. 21 Issue 8, pN.PAG-N.PAG. 24p. - Publication Year :
- 2019
-
Abstract
- In this paper, we study Hardy's inequality in a limiting case: ∫ Ω | ∇ u | N d x ≥ C N (Ω) ∫ Ω | u (x) | N | x | N (log R | x |) N d x for functions u ∈ W 0 1 , N (Ω) , where Ω is a bounded domain in ℝ N with R = sup x ∈ Ω | x |. We study the attainability of the best constant C N (Ω) in several cases. We provide sufficient conditions that assure C N (Ω) > C N (B R) and C N (Ω) is attained, here B R is the N -dimensional ball with center the origin and radius R. Also, we provide an example of Ω ⊂ ℝ 2 such that C 2 (Ω) > C 2 (B R) = 1 / 4 and C 2 (Ω) is not attained. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RADIUS (Geometry)
*MATHEMATICAL equivalence
*BLOWING up (Algebraic geometry)
Subjects
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 21
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 139213532
- Full Text :
- https://doi.org/10.1142/S0219199718500700