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:
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