Sobolev Mapp&gs with Integrable Dilatations
نویسندگان
چکیده
We show that each quasi-light mapping f i n the Sobolev space W~'n(s R n) satisfying ]Df(x)ln<=K(x,f)J(x,f) for almost every x and for some K~Lr(s r > n 1, is open and discrete. The assumption that f be quasilight can be dropped if, in addition, it is required that f~ WI'P(f2, R n) for some p ___ n + 1/(n 2). More generally, we consider mappings in the John Ball classes dp, q(s and give conditions that guarantee their discreteness and openness.
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