197 research outputs found
On the Sobolev trace Theorem for variable exponent spaces in the critical range
In this paper we study the Sobolev Trace Theorem for variable exponent spaces
with critical exponents. We find conditions on the best constant in order to
guaranty the existence of extremals. Then we give local conditions on the
exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to
satisfy such conditions, and therefore to ensure the existence of extremals.Comment: 21 pages, submitte
Existence of solution to a critical equation with variable exponent
In this paper we study the existence problem for the Laplacian
operator with a nonlinear critical source. We find a local condition on the
exponents ensuring the existence of a nontrivial solution that shows that the
Pohozaev obstruction does not holds in general in the variable exponent
setting. The proof relies on the Concentration--Compactness Principle for
variable exponents and the Mountain Pass Theorem
Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces
We study the continuity and compactness of embeddings for radial Besov and
Triebel-Lizorkin spaces with weights in the Muckenhoupt class . The
main tool is a discretization in terms of an almost orthogonal wavelet
expansion adapted to the radial situation
- …