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Sobolev functions on infinite-dimensional domains |
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| Authors: | Vladimir I Bogachev Andrey Yu Pilipenko Alexander V Shaposhnikov |
| Institution: | 1. Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia;2. National Research University, Higher School of Economics, Moscow, Russia;3. Institute of Mathematics NAS, 3, Tereschenkivska st., 01601 Kiev, Ukraine |
| 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. |
| Keywords: | Sobolev class Extension Differentiable measure Gaussian measure |
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