SOBOLEV MAPPINGS WITH INTEGRABLE DILATATIONS

We show that each quasi-light mapping f in the Sobolev space W1,n (OME GA, R(n)) satisfying \Df(x)\n less-than-or-equal-to K(x,f)J(x,f) for a lmost every x and for some K is-an-element-of L(r) (OMEGA), r > n - 1, is open and discrete. The assumption that f be quasi-light can be dro pped if, in addition, it is required that f is-an-element-of W1,P (OME GA, R(n)) for some p greater-than-or-equal-to n + 1 / (n - 2). More ge nerally, we consider mappings in the John Ball classes A(p,q)(OMEGA), and give conditions that guarantee their discreteness and openness.