科研之友
微信
新浪微博
Facebook
分享链接
摘要
Let D be a bounded domain in R-n, n %26gt;= 2, and let f be a continuous mapping of (D) over bar into R-n which is quasiconformal in D. Suppose that vertical bar f(x) - f(y)vertical bar %26lt;= omega(vertical bar x-y vertical bar) for all x and y in partial derivative D, where omega is a non-negative non-decreasing function satisfying omega(2t) %26lt;= 2w(t) for t %26gt;= 0. We prove, with an additional growth condition on omega, that vertical bar f(x) - f(y)vertical bar %26lt;= C max{omega(vertical bar x - y vertical bar), vertical bar x - y vertical bar(alpha)} for all x, y is an element of D, where alpha = K-1(f)(1/(1-n)).
- 出版日期2012
