Various characterizations of optimal Sobolev trace Embeddings

Abstract EN

We exhibit and describe optimal target spaces in orbitrary- order Sobolev type embedding's for traces of nn-dimensional functions on lower dimensional subspaces, this method is very efficient to give various characterizations of optimal Sobolev trace embedding's, we used the descriptive-deductive method, Results: we found that any trace embedding can be reduced to a one-dimensional inequality for a Hardy type operator depending only on nn and on the dimension of the relevant subspace.