Bulletin of the Australian Mathematical Society

Research Article

On the sharpness of a limiting case of the Sobolev imbedding theorem

J. A. Hempela1, G. R. Morrisa2 and N. S. Trudingera3

a1 University of New England, Armidale, New South Wales;

a2 University of New England, Armidale, New South Wales;

a3 University of Queensland, St Lucia, Queensland.

Abstract

A refinement of the Sobolev imbedding theorem, due to Trudinger, is shown to be optimal in a natural sense.

(Received August 10 1970)