On W~(1, p(x)) versus C~1 local minimizers of functionals related to p(x)-Laplacian

摘要

Let Ω be a bounded domain in IR~N, N≥2 with smooth boundary. We consider the functional J: W~(1, p(x))(Ω)→IR defined as J(u)=∫_Ω(|{nabla}u|~(p(x))/p(x)+∫_Ω((|u|~p(x))/p(x))-∫_Ω(F(x,u))-∫_{partial deriv}Ω(G(x,u)dσ), where p(x) be a Holder continuous function satisfying 1(x)≤N in Ω{top}- and F(x, t) =∫f(x,s)ds, 0