Geodesic
Some remarks on the mollification of piecewise-linear homeomorphisms
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 235-242 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct an example of a piecewise positive (a.e.) Jacobian such that the usual convolution does not preserve the sign of the Jacobian. Bibliography: 4 titles. 
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     author = {G. A. Seregin and T. N. Shilkin},
     title = {Some remarks on the mollification of piecewise-linear homeomorphisms},
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     pages = {235--242},
     year = {1995},
     volume = {221},
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G. A. Seregin; T. N. Shilkin. Some remarks on the mollification of piecewise-linear homeomorphisms. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 235-242. http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a14/