by Gazzola, F., Grunau, H.-Ch., Sweers, G..
Series: 2009-17, Preprints
We prove that the best constant for the critical embedding of higher order
Sobolev spaces does not depend on all the traces. The proof uses a
comparison principle due to Talenti and an extension
argument which enables us to extend radial functions from the ball to the whole
space with no increase of the Dirichlet norm. Similar arguments may also be
used to prove the very same result for Hardy-Rellich inequalities.
optimal constant, Sobolev embedding, Hardy-Rellich inequality