Solutions of Elliptic Inequalities That Vanish in a Neighborhood of Infinity. Case of Critical Dimension

摘要

Let Ω be an unbounded open subset of R~n, n ≥ 2. By B_r and S_r we denote the open ball and the sphere, respectively, of radius r centered at the origin. As in [6], W_(p,loc)~1(Ω K), p > 1, stands for the space of measurable functions belonging to W_p~1 (B_r ∩ Ω K) for all reals r > 0 satisfying the condition B_r ∩ Ω K ≠ ?. The space L_(p,loc)(Ω K) is defined in a similar way.