We consider the functionalF(u) = integral(Omega)f(x, Du(x))dx,where f (x, z) satisfies a (p, q)-growth condition with respect to z and can be approximated by means of a suitable sequence of functions. We consider B-R (sic) Omega and the spacesX = W-1,W-p(B-R, R-N) and Y = W-1,W-p(B-R, R-N) boolean AND W-loc(1,q)(B-R, R-N).We prove that the lower semicontinuous envelope of F|(Y) coincides with F or, in other words, that the Lavrentiev term is equal to zero for any admissible function u is an element of W-1,W-q(B-R, R-N). We perform the approximations by means of functions preserving the values on the boundary of B-R.

Nonoccurrence of Lavrentiev gap for a class of functionals with nonstandard growth

De Filippis F.;Leonetti F.;
2024-01-01

Abstract

We consider the functionalF(u) = integral(Omega)f(x, Du(x))dx,where f (x, z) satisfies a (p, q)-growth condition with respect to z and can be approximated by means of a suitable sequence of functions. We consider B-R (sic) Omega and the spacesX = W-1,W-p(B-R, R-N) and Y = W-1,W-p(B-R, R-N) boolean AND W-loc(1,q)(B-R, R-N).We prove that the lower semicontinuous envelope of F|(Y) coincides with F or, in other words, that the Lavrentiev term is equal to zero for any admissible function u is an element of W-1,W-q(B-R, R-N). We perform the approximations by means of functions preserving the values on the boundary of B-R.
File in questo prodotto:
File Dimensione Formato  
F_DeFilippis-Leonetti-Treu_Adv_Nonlin_Anal2024.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 2.79 MB
Formato Adobe PDF
2.79 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

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/11697/236919
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 2
social impact