Abstract

Let H be a separable Hilbert space and let A A ⊂ H → H be a self-adjoint operator with A ≤ I, > 0 and Tr −A −1 < . We endow H with the centered Gaussian measure with covariance operator Q = − 2 1 A −1 and consider a function U ∈ C 3 H with bounded second and third order derivatives, the SDE dX = AX − DU X dt + dW t , X 0 = x and the associated transition semigroup P t . We define the class BV H of bounded variation functions with respect to the probability measure dx = Z −1 e −2U x dx , where Z is the normalization constant, through an integration by parts formula and prove that P t u ∈ W 1 1 H for t > 0, u ∈ BV H , and that u ∈ BV H if and only if the limit of DP t u L 1 H as t → 0 is finite.

Autore Pugliese

• Pallara Diego

Tutti gli autori

• Ambrosio L. , Da Prato G. , Goldys B. , Pallara D.

Titolo volume/Rivista

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Anno di pubblicazione

2012

ISSN

0360-5302

ISBN

Non Disponibile

Numero di citazioni Wos

2

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

1

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile