ABSTRACT
We are given a real separable Hilbert space H (norm ∣ · ∣, inner product (·,·),) a selfadjoint strictly negative operator A : D(A) ⊂ H → H such that A −1 is of trace class, and 〈 A x , x 〉 ≤ − ω | x | 2 , x ∈ H , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/eqn_chapter_40_1_1.tif"/> for some ω > 0, and a convex proper lower semicontinuous mapping U : H → [0, + ∞]. For any x ∈ H we denote by E(x) the subdifferential of U: E ( x ) = { z ∈ H : U ( x + y ) ≥ U ( x ) + 〈 y , z 〉 , ∀ y ∈ H } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/equ_chapter40_483_1.tif"/> and set D ( E ) = { x ∈ H : E ( x ) ≠ ∅ } . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/equ_chapter40_483_2.tif"/>
