Geodesic
An introduction to composition operators in Sobolev spaces
Eurasian mathematical journal, Tome 14 (2023) no. 1, pp. 39-54

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We propose a survey of the results on the composition operators in classical Sobolev spaces, obtained between 1975 and 2020. A first version of these notes were the subject of a series of lectures, given in Padova University in January 2018. 
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G. Bourdaud. An introduction to composition operators in Sobolev spaces. Eurasian mathematical journal, Tome 14 (2023) no. 1, pp. 39-54. http://geodesic.mathdoc.fr/item/EMJ_2023_14_1_a3/