On the structure of Hardy–Sobolev–Maz'ya inequalities

We establish new improvements of the optimal Hardy inequality in the half-space. We ﬁrst add all possible linear combinations of Hardy type terms, thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and su...

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Veröffentlicht in:	Journal of the European Mathematical Society : JEMS 2009-01, Vol.11 (6), p.1165-1185
Hauptverfasser:	Filippas, Stathis, Tertikas, Achilles, Tidblom, Jesper
Format:	Artikel
Sprache:	eng
Schlagworte:	Partial differential equations
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We establish new improvements of the optimal Hardy inequality in the half-space. We ﬁrst add all possible linear combinations of Hardy type terms, thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufﬁcient conditions for the validity of Hardy–Sobolev–Maz’ya type inequalities.
ISSN:	1435-9855 1435-9863
DOI:	10.4171/JEMS/178