Best constants in Sobolev trace inequalities

In this paper we establish the best constant for a Sobolev trace inequality on compact Riemannian manifolds with boundary. More specifically, let I < p < n and [GRAPHICS] where (p) over bar* = p(n - I)1(n - p). We prove that for any compact n-dimensional Riemannian manifold with boundary (M, g), for any epsilon > 0 there exists A(epsilon) > 0 such that \\u\\(P)(L (p) over bar*)(partial derivativeM) less than or equal to ((K) over bar (n,p) + epsilon) \\del(g)u\\(p)(Lp(M)) + Aepsilon\\u\\(p)(Lp(partial derivativeM)) for all u is an element of H-1,H-p (M). (C) 2003 Elsevier Science Ltd. All rights reserved.