Otto-von-Guericke-Universität Magdeburg

 
 
 
 
 
 
 
 

09-17

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

 

Preprint series: 09-17, Preprints

MSC:
46E35 Sobolev spaces and other spaces of ``smooth\'\' functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
35J55 Boundary value problems for elliptic systems

 

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


The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.

Letzte Änderung: 10.02.2016 - Ansprechpartner: Pierre Krenzlin