Canceling effects in higher-order Hardy–Sobolev inequalities

Andrea Cianchi, Norisuke Ioku

Research output: Contribution to journalArticlepeer-review


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 L1.

Original languageEnglish
Article number31
JournalCalculus of Variations and Partial Differential Equations
Issue number2
Publication statusPublished - 2017 Apr 1
Externally publishedYes


  • 46E30
  • 46E35

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Canceling effects in higher-order Hardy–Sobolev inequalities'. Together they form a unique fingerprint.

Cite this