We study the realization A_N of the operator A = 1/2 \Delta - < DU , D\cdot > in L^2(Omega, mu) with Neumann boundary condition, where Omega is a possibly unbounded convex open set in R^N, U is a convex unbounded function, DU(x) is the element with minimal norm in the subdifferential of U at x, and mu(dx) = c exp(-2U(x))dx is a probability measure, infinitesimally invariant for A. We show that A_N is a dissipative self-adjoint operator in L^2(Omega, mu). Log-Sobolev and Poincare' inequalities allow then to study smoothing properties and asymptotic behavior of the semigroup generated by A_N.

Elliptic operators with unbounded drift coefficients and Neumann boundary condition / G., Da Prato; Lunardi, Alessandra. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 198:(2004), pp. 35-52. [10.1016/j.jde.2003.10.025]

Elliptic operators with unbounded drift coefficients and Neumann boundary condition

LUNARDI, Alessandra
2004-01-01

Abstract

We study the realization A_N of the operator A = 1/2 \Delta - < DU , D\cdot > in L^2(Omega, mu) with Neumann boundary condition, where Omega is a possibly unbounded convex open set in R^N, U is a convex unbounded function, DU(x) is the element with minimal norm in the subdifferential of U at x, and mu(dx) = c exp(-2U(x))dx is a probability measure, infinitesimally invariant for A. We show that A_N is a dissipative self-adjoint operator in L^2(Omega, mu). Log-Sobolev and Poincare' inequalities allow then to study smoothing properties and asymptotic behavior of the semigroup generated by A_N.
2004
Elliptic operators with unbounded drift coefficients and Neumann boundary condition / G., Da Prato; Lunardi, Alessandra. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 198:(2004), pp. 35-52. [10.1016/j.jde.2003.10.025]
File in questo prodotto:
File Dimensione Formato  
NeumannJDE2004.pdf

non disponibili

Tipologia: Documento in Post-print
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 289.29 kB
Formato Adobe PDF
289.29 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1441817
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 34
  • ???jsp.display-item.citation.isi??? 34
social impact