SOBOLEV EMBEDDINGS FOR UNBOUNDED DOMAIN WITH VARIABLE EXPONENT HAVING VALUES ACROSS N

We study Sobolev embeddings for unbounded domain with variable exponent having values across N. A main result of this paper is the following theorem: Let Omega be an unbounded domain in RN satisfying the uniform cone condition. Suppose that p : Omega -> R is Lipschitz and 1 L-q(.) (Omega) for any q is an element of L-infinity(Omega) satisfying condition p(x) = N. In this theorem the usual condition sup p(x) < N is not required.