科研之友
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摘要
Suppose that Omega subset of R-n is a domain with n >= 2. We show that a continuous, sense-preserving, open and discrete mapping of finite geometric outer distortion with kappa(O)(.,f) is an element of L-loc(1/(n-1))(Omega) is absolutely continuous on almost every line parallel to the coordinate axes. Moreover, if U subset of Omega is an open set with N(f,U) < infinity, then f satisfies the distortion inequality vertical bar Df(x)vertical bar(n) <= C vertical bar J(x,f)vertical bar kappa(O)(x,f) for almost every x is an element of U, where the constant C > 0 depends only on n and on the maximum multiplicity N(f, U).
- 出版日期2015
