Uniform limits of certain A-harmonic functions with applications to quasiregular mappings
1991; Finnish Academy of Science and Letters; Volume: 16; Linguagem: Inglês
10.5186/aasfm.1991.1609
ISSN0066-1953
AutoresAlexandre Erëmenko, John L. Lewis,
Tópico(s)Advanced Harmonic Analysis Research
ResumoLet u1, 1t2t...ru* be nonconstant uniform limits (on compact subsets) of ,4 harmonic functions in {c : lrl < n} C R' where .4satisfies certain elliptic structure conditions.Theauthorsshowthatifthereexistsl20suchthat(i) {c:u;(n) <-)}n{c:u1@)< -)}=0, (ii)luf-"ll Sl,and(iii)lu,(O)l (),forl<i,,i(rn,thenrn(cwherecdependsonly on thä structure conditions and n.As an application they show that their theorem provides a completely P.D.E.proof of Rickman's generalization of Picard's theorem to quasiregular mappings. IntroductronLet u: (rr,...,nn) denote apoint in Euclidean n space (R"), andput (*, y) riyi, fr,,U € R', B(r,r):{u:ly-"1 <r}, r)0, r€R'.Let E, 08, and lEl denote the closure, boundary, and Lebesgue n measure of E.lf.g is afunction on R', put M(r, g,to): sup g, gi : mil(g,0) and B(xs,r) t0s 0g 0gt v9: \Arr
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