We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W-0(s,p)(Omega) hooked right arrow L-q(Omega),where N >= 1 , 0 < s < 1 , p = 1,2 , 1 <= q < p(s )(& lowast;)= Np/N - sp , and Omega subset of R(N )is a bounded smooth domain or the whole space RN . Our results cover the borderline case p = 1 , the Hilbert case p = 2 , N > 2s , and the so-called Sobolev limiting case N = 1 , s = (1/)(2 ), and p=2 , where a sharp asymptotic estimate is given by means of a limiting procedure. We apply the obtained results to prove existence and non-existence of solutions for a wide class of nonlocal partial differential equations.

Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs

Cassani D.
;
Du L.
2023-01-01

Abstract

We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W-0(s,p)(Omega) hooked right arrow L-q(Omega),where N >= 1 , 0 < s < 1 , p = 1,2 , 1 <= q < p(s )(& lowast;)= Np/N - sp , and Omega subset of R(N )is a bounded smooth domain or the whole space RN . Our results cover the borderline case p = 1 , the Hilbert case p = 2 , N > 2s , and the so-called Sobolev limiting case N = 1 , s = (1/)(2 ), and p=2 , where a sharp asymptotic estimate is given by means of a limiting procedure. We apply the obtained results to prove existence and non-existence of solutions for a wide class of nonlocal partial differential equations.
2023
fractional Sobolev spaces; best constants; fractional Laplacian; nonlocal PDEs; asymptotic analysis; variational methods
Cassani, D.; Du, L.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2164351
 Attenzione

L'Ateneo sottopone a validazione solo i file PDF allegati

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact