by Gazzola, F., Grunau, H.-Ch., Sweers, G..

**Series:** 2009-17, Preprints

- MSC:
- 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
- 26D10 Inequalities involving derivatives and differential and integral operators

**Abstract:**

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.

**Keywords:**

optimal constant, Sobolev embedding, Hardy-Rellich inequality