Title Regular selections for multiple-valued functions. Publication Type Journal Article Year of Publication 2004 Authors De Lellis C., Grisanti C.R, Tilli P. Journal Annali di Matematica Pura ed Applicata Volume 183 Pagination 79–95 Publisher Ann. Mat. Pura Appl. Type of Article Q-valued ISSN 0373-3114 Keywords differentiability, modulus of continuity Abstract Given a multiple-valued function f, we deal with the problem of selecting its single valued branches. This problem can be stated in a rather abstract setting considering a metric space E and a finite group G of isometries of E. Given a function f which takes values in the equivalence classes of E/G, the problem consists in finding a map g with the same domain as f and taking values in E, such that at every point t the equivalence class of g(t) coincides with f(t). If the domain of f is an interval, we show the existence of a function g with these properties which, moreover, has the same modulus of continuity of f. In the particular case where E is the product of Q copies of $R$ n and G is the group of permutations of Q elements, it is possible to introduce a notion of differentiability for multiple valued functions. In this case, we prove that the function g can be constructed in such a way to preserve C k,\ensuremathα regularity. Some related problems are also discussed. Notes Ann. Mat. Pura Appl. (4) 183 (2004), no. 1, 79–95. URL http://www.springerlink.com/content/hny2gvjembvuth8p/ DOI 10.1007/s10231-003-0081-5
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