Abstract.Let F e ^^'"(ß; K") be a mapping with nonnegative JacobianJf (x) = det DF(x) > 0 for a.e. x in a domain Í2 c R" . The dilatation of F is defined (almost everywhere in Í2) by the formulaIwaniec and Sverák [IS] have conjectured that if p > n -1 and K e Lfoc(f2) then F must be continuous, discrete and open. Moreover, they have confirmed this conjecture in the two-dimensional case n -2 . In this article, we verify it in the higher-dimensional case n > 2 whenever p > n -1 .

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Let F ∈ W 1,n loc (Ω; R n ) be a mapping with non negative Jacobian J F (x) = detDF (x) ≥ 0 for a. e. x in a domain Ω ⊂ R n . The dilatation of F is defined (almost everywhere in Ω) by the formula

Abstract. In this paper we discuss two different topics concerning Aharmonic functions. These are weak solutions of the partial differential equation, the function β is bounded and α(x) > 0 for a.e. x. First, we present a new approach to the regularity of A-harmonic functions for p > n−1. Secondly, we establish results on the existence of nontangential limits for A-harmonic functions in the Sobolev space W 1,q (B), for some q > 1, where B is the unit ball in R n . Here q is allowed to be different from p.