On the extremal functions of Sobolev–Poincaré inequality

Meijun Zhu

Vol. 214 (2004), No. 1, 185–199

DOI: 10.2140/pjm.2004.214.185

Abstract

We prove the existence of extremal functions of Sobolev-Poincaré inequality on Sⁿ for p ∈ (1,(1 + )∕4). For general n-dimensional compact Riemannian manifolds embedded in Rⁿ⁺¹, such an existence result is proved for p ∈ (n∕(n− 1),(1 + )∕4).

Milestones

Received: 6 February 2003

Revised: 2 June 2003

Published: 1 March 2004