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 a contribution of Castro-DavilaYang , where a canceling phenomenon underling the relevant inequalities was discovered in the special case of functions with derivatives in L^1..
Canceling effects in higher-order Hardy-Sobolev inequalities / Cianchi, Andrea; Ioku, Norisuke. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 56:(2017), pp. 1-18.
Canceling effects in higher-order Hardy-Sobolev inequalities
CIANCHI, ANDREA;
2017
Abstract
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 a contribution of Castro-DavilaYang , where a canceling phenomenon underling the relevant inequalities was discovered in the special case of functions with derivatives in L^1..I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.