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Статья

Sobolev functions on infinite-dimensional domains

Journal of Mathematical Analysis and Applications . 2014. Vol. 419. No. 2. P. 1023-1044.
Bogachev V., Pilipenko A. Y., Shaposhnikov A.

We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we  present a negative solution of the long-standing problem of existence of  Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.