Numerical computation of least constants for the Sobolev inequality

Summary Least constantsc for the well-known Sobolev inequality fcf_{m, G},fH^m(G) are obtained in closed form by a reproducing kernel technique, where the Sobolev spaceH^m(G) for a domainG in ⁿ is defined as the completion ofC^m(G) with respect to the Sobolev norm given by, where is the norm ofL₂(G) and is the supremum norm onG. Numerical values for the case whereG is the ⁿ are given.