Improved Sobolev inequality under constraints

Abstract

We give a new proof of Aubin's improvement of the Sobolev inequality on ${\mathbb{S}}^n$ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on ${\mathbb{S}}^n$, we determine the constant explicitly in the second order moments case.

25 pages. Typos corrected, references added, to appear in IMRN

References in corpus (2)

• Sign of Green's function of Paneitz operators and the Q curvature
• Cubature formulas and Sobolev inequalities

Cited by in corpus (1)

• Cubature formulas and Sobolev inequalities