Traces of Sobolev functions on regular surfaces in infinite dimensions

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• 作者：Pietro Celada ; Aless ; ra Lunardi
• 关键词：Infinite dimension analysis ; Sobolev spaces ; Surface measures ; Traces
• 刊名：Journal of Functional Analysis
• 出版年：15 February, 2014
• 年：2014
• 卷：266
• 期：4
• 页码：1948-1987
• 全文大小：504 K

文摘

In a Banach space X endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set of a Sobolev nondegenerate function . We define the traces at of the elements of for , as elements of where 蟻 is the surface measure of Feyel and de La Pradelle. The range of the trace operator is contained in for and even in under further assumptions. If is a suitable halfspace, the range is characterized as a sort of fractional Sobolev space at the boundary. An important consequence of the general theory is an integration by parts formula for Sobolev functions, which involves their traces at .