1 research outputs found
Limiting behaviour of intrinsic semi-norms in fractional order Sobolev spaces
We collect and extend results on the limit of as tends to or , where
is or a smooth bounded domain, is 0 or 1, is a
nonnegative integer, , and is the
intrinsic semi-norm of order in the Sobolev space
. In general, the above limit is equal to ,
where and are, respectively, a constant and a semi-norm that we
explicitly provide. The particular case for is also
examined and the results are then proved by using the Fourier transform.Comment: LaTeX, document class is amsart, 15 pages. Submitted to Studia
Mathematic