• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

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.