Extension of a homeomorphism

Does every homeomorphism of the unit sphere S^n, n=2, has diffeomorphic extension to the unit ball. I am indeed interesten about the reference of the following problem: I need a given homeomorphism $h$ of the unit sphere to approximate uniformly by a sequence of diffeomorphisms $h_i$.

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Presumably, you are looking for a homeomorphism of the unit ball whose restriction to the interior is a diffeomorphism, and whose restriction to the boundary is your given homeomorhpism. –  André Henriques Jul 12 '11 at 11:31
I'm guessing that the answer is "yes" for $n=2$. The question is also interesting for other values of $n$... where the answer will probably be negative (but I don't know for sure). –  André Henriques Jul 12 '11 at 11:36

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David Kalaj posted the following comments in a (now-deleted) answer: (1) Thanks. Yes this was the point of my question. I need a reference for this. (2) It seems that this, the answer to the question: For a given homeomorphism h of the unit sphere find sequence of diffeomorphisms h_i of the sphere that converges uniformly to h is YES, but i need a reference –  Anton Geraschenko Jul 12 '11 at 16:31
These comments do not seem to make sense. Am I missing something? –  Igor Rivin Jul 12 '11 at 18:33