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arXiv · 1309.5475

Sobolev functions on infinite-dimensional domains

Vladimir I. Bogachev·Andrey Yu. Pilipenko·Alexander V. Shaposhnikov
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Abstract

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.

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Vladimir I. Bogachev, Andrey Yu. Pilipenko, Alexander V. Shaposhnikov. 2013-09-21. Sobolev functions on infinite-dimensional domains. https://arxiv.org/abs/1309.5475

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