AbstractThe article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: Ws,p→Lpn/(n−sp) as s↑1 and s↑n/p. Their result is extended to all values of s∈(0,1) and is supplied with an elementary proof. The relationlims↓0s∫Rn∫Rn∣u(x)−u(y)∣p∣x−y∣n+spdxdy=2p−1∣Sn−1∣∥u∥pLp(Rn) is proved
Explicit upper and lower estimates are given for the norms of the operators of embedding of W̊2 n(-1...
This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of...
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on...
Communicated by H. Brezis. ABSTRACT. Generalizations of Trudinger's and Br•zis-Wainger's l...
This article is devoted to the investigation of some properties of Sobolev spaces with mixed norm. ©...
We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W0s,p(Ω...
We obtain an improved Sobolev inequality in $H^s$ spaces involving Morrey norms. This refinement yie...
We establish upper and lower estimates for the embedding constants related to the classical Sobolev ...
$ (-\varDelta)_{p(\cdot)}^{s(\cdot)}u+V(x)|u|^{p(x)-2}u = f(x,u)+g(x) $ where $ x\in\Omega\subs...
It is known that the Sobolev space W-1,W-P(R-N) is embedded into LNP/(N-P)(R-N) if p < N and into...
In this paper we study how the (normalised) Gagliardo semi-norms [u]Ws,p(Rn) control translations. I...
Extended erratum to ``On some questions of topology for $S^1$-valued fractional Sobolev spaces'' of ...
We study the properties of Sobolev functions and mappings, especially we study the violation of some...
Consider the Sobolev embedding operator from the space of functions in W-1,W-p(I) with average zero ...
In this note we demonstrate the Brezis-Ponce method to prove an embedding theorem for the fractional...
Explicit upper and lower estimates are given for the norms of the operators of embedding of W̊2 n(-1...
This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of...
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on...
Communicated by H. Brezis. ABSTRACT. Generalizations of Trudinger's and Br•zis-Wainger's l...
This article is devoted to the investigation of some properties of Sobolev spaces with mixed norm. ©...
We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W0s,p(Ω...
We obtain an improved Sobolev inequality in $H^s$ spaces involving Morrey norms. This refinement yie...
We establish upper and lower estimates for the embedding constants related to the classical Sobolev ...
$ (-\varDelta)_{p(\cdot)}^{s(\cdot)}u+V(x)|u|^{p(x)-2}u = f(x,u)+g(x) $ where $ x\in\Omega\subs...
It is known that the Sobolev space W-1,W-P(R-N) is embedded into LNP/(N-P)(R-N) if p < N and into...
In this paper we study how the (normalised) Gagliardo semi-norms [u]Ws,p(Rn) control translations. I...
Extended erratum to ``On some questions of topology for $S^1$-valued fractional Sobolev spaces'' of ...
We study the properties of Sobolev functions and mappings, especially we study the violation of some...
Consider the Sobolev embedding operator from the space of functions in W-1,W-p(I) with average zero ...
In this note we demonstrate the Brezis-Ponce method to prove an embedding theorem for the fractional...
Explicit upper and lower estimates are given for the norms of the operators of embedding of W̊2 n(-1...
This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of...
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on...