| Popis: |
In a Banach space X endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set O = { x ∈ X : G ( x ) 0 } of a Sobolev nondegenerate function G : X ↦ R . We define the traces at G − 1 ( 0 ) of the elements of W 1 , p ( O , μ ) for p > 1 , as elements of L 1 ( G − 1 ( 0 ) , ρ ) where ρ is the surface measure of Feyel and de La Pradelle. The range of the trace operator is contained in L q ( G − 1 ( 0 ) , ρ ) for 1 ⩽ q p and even in L p ( G − 1 ( 0 ) , ρ ) under further assumptions. If O 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 G − 1 ( 0 ) . |
