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Abstract
The aim of this paper is to give an identification of the Sobolev spaces Wk,p(Rn) intrinsically in terms of the Sobolev spaces W0k,p(Br(0)) of functions defined in the ball Br(0) of center zero and radius r>0. To provide such identification we make use of the category theoretic concept of colimit. We apply these techniques to certain examples of nonlinear differential equations.
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