Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 56, Issue 2, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-017-1112-1
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Funding
- MIUR (Italian Ministry of Education, University and Research) Prin Elliptic and parabolic partial differential equations: geometric aspects, related inequalities, and applications [2012TC7588]
- GNAMPA of the Italian INdAM (National Institute of High Mathematics)
- JSPS KAKENHI [25220702]
- Grants-in-Aid for Scientific Research [15K17575, 17K05333] Funding Source: KAKEN
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A classical first-order Hardy-Sobolev inequality in Euclidean domains, involving weighted norms depending on powers of the distance function from their boundary, is known to hold for every, but one, value of the power. We show that, by contrast, the missing power is admissible in a suitable counterpart for higher-order Sobolev norms. Our result complements and extends contributions by Castro and Wang (Calc Var 39(3-4): 525-531, 2010), and Castro et al. (Comptes Rendus Math Acad Sci Paris 349: 765-767, 2011; J Eur Math Soc 15: 145-155, 2013), where a surprising canceling phenomenon underling the relevant inequalities was discovered in the special case of functions with derivatives in L-1.
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