Sobolev functions on infinite-dimensional domains
Vladimir Igorevich Bogachev, Andrey Yurievich Pilipenko, A. V. Shaposhnikov · arXiv (Cornell University) · 2013
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.