[Authors]
 A. I. Nazarov, A. B. Reznikov

[Title]
 On the existence of an extremal function in critical Sobolev trace embedding theorem

[AMS Subj-class]
 49J10 Free problems in two or more independent variables
 35J20 Variational methods for second-order, elliptic equations

[Keywords]
 minimizers; trace Sobolev embedding; critical exponent; 
 trace Sobolev--Poincar\'e inequality; $p$-Laplacian

[Abstract]
 Sufficient conditions for the existence of extremal functions in the trace 
 Sobolev inequality and the trace Sobolev--Poincar\'e inequality are established. 
 It is shown that some of these conditions are sharp. 

[Comments]
 English, 15 pp.

[Contact e-mail]
 al.il.nazarov@gmail.com