Sobolev inequalities for variable exponents attaining the values 1 and $n$
Sobolev inequalities for variable exponents attaining the values 1 and $n$
We study Sobolev embeddings in the Sobolev space W 1,p(•) (Ω) with variable exponent satisfying 1 p(x) n.Since the exponent is allowed to reach the values 1 and n, we need to introduce new techniques, combining weak-and strong-type estimates, and a new variable exponent target space scale which features a …