A. Lunardi

activity

20082021

most citedInvariant Measures and Maximal L^2 Regularity for Nonautonomous Ornstein-Uhlenbeck Equations

25 citations · 78 across the 16 of their papers we have counts for

collaborators

22 papers

math.PR2021★ 1 cited

Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension

Sandra Cerrai, Alessandra Lunardi

We prove smoothing properties and optimal Schauder type estimates for a class of nonautonomous evolution equations driven by time dependent Ornstein-Uhlenbeck operators in a separa…

math.FA2020

Time regularity for generalized Mehler semigroups

Alessandra Lunardi

We study continuity and Hölder continuity of $t \mapsto P_{t} f$ , where $P_{t}$ is a generalized Mehler semigroup in $C_{b} (X)$ , the space of the continuous and bounded functions from a Ba…

math.AP2019★ 18 cited

Schauder theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces

Alessandra Lunardi, Michael Röckner

We prove maximal regularity results in Hölder and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential opera…

math.AP2019

Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension

Sandra Cerrai, Alessandra Lunardi

We prove Schauder type estimates for stationary and evolution equations driven by the classical Ornstein-Uhlenbeck operator in a separable Banach space, endowed with a centered Gau…

math.PR2018

On the law of the minimum of the solutions to a class of unidimensional SDEs

Giuseppe Da Prato, Alessandra Lunardi, Luciano Tubaro

We prove that the law of the minimum $m := min_{t \in [0, 1]} ξ (t)$ of the solution $ξ$ to a one-dimensional ODE with good nonlinearity has continuous density with respect to the Lebes…

math.FA2018

BV functions in Hilbert spaces

Giuseppe Da Prato, Alessandra Lunardi

We study $B V$ functions in a Hilbert space $X$ endowed with a probability measure $ν$ , assuming that $ν$ is Fomin differentiable along suitable directions. We establish basic chara…

math.PR2016

Malliavin Calculus for non Gaussian differentiable measures and surface measures in Hilbert spaces

Giuseppe Da Prato, Alessandra Lunardi, Luciano Tubaro

We construct surface measures in a Hilbert space endowed with a probability measure $ν$ . The theory fits for invariant measures of some stochastic partial differential equations su…

math.PR2016

Averaging principle for non autonomous slow-fast systems of stochastic RDEs: the almost periodic case

Sandra Cerrai, Alessandra Lunardi

We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend…

math.AP2015

Strong convergence of solutions to nonautonomous Kolmogorov equations

Luca Lorenzi, Alessandra Lunardi, Roland Schnaubelt

We study a class of nonautonomous, linear, parabolic equations with unbounded coefficients on $R^{d}$ which admit an evolution system of measures. It is shown that the solu…

math.AP2015

Semilinear nonautonomous parabolic equations with unbounded coefficients in the linear part

Luciana Angiuli, Alessandra Lunardi

We study the Cauchy problem for the semilinear nonautonomous parabolic equation $u_{t} = A (t) u + ψ (t, u)$ in $[s, τ] \times R^{d}$ , $τ > s$ , in the spaces $C_b([s, τ]\ti…

math.PR2014

Surface measures in infinite dimension

Giuseppe Da Prato, Alessandra Lunardi, Luciano Tubaro

We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.

math.FA2014

BV functions on convex domains in Wiener spaces

Alessandra Lunardi, Michele Miranda, Diego Pallara

We study functions of bounded variation defined in an abstract Wiener space X, relating the variation of a function u on a convex open set O in X to the behavior near t=0 of T(t)u,…

math.AP2013

Maximal Sobolev regularity in Neumann problems for gradient systems in infinite dimensional domains

Giuseppe Da Prato, Alessandra Lunardi

We consider an elliptic Kolmogorov equation lambda u - Ku =f in a convex subset C of a separable Hilbert space X. We prove maximal Sobolev regularity of its weak solution, when lam…

math.AP2013

Traces of Sobolev functions on regular surfaces in infinite dimensions

Pietro Celada, Alessandra Lunardi

In a Banach space $X$ endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set $O = {x \in X : G (x) < 0}$ of a Sobolev n…

math.AP2012★ 2 cited

Sobolev regularity for a class of second order elliptic PDE's in infinite dimension

Giuseppe Da Prato, Alessandra Lunardi

We consider an elliptic Kolmogorov equation $λ u - K u = f$ in a separable Hilbert space $H$ . The Kolmogorov operator $K$ is associated to an infinite dimensional convex gradient sys…

math.AP2012★ 5 cited

Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

L. Angiuli, L. Lorenzi, A. Lunardi

We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I \times R^{d}$ , where $I$ is a right-halfline. We prove logarithmic Sobo…

math.AP2012★ 2 cited

Maximal $L^{2}$ regularity for Dirichlet problems in Hilbert spaces

Giuseppe Da Prato, Alessandra Lunardi

We consider the Dirichlet problem $λ U - L U = F$ in \mathcal{O}, U=0 on $\partial O$ . Here $F \in L^{2} (O, μ)$ where $μ$ is a nondegenerate centered Gaus…

math.FA2011

Perimeter of sublevel sets in infinite dimensional spaces

Vicent Caselles, Alessandra Lunardi, Michele Miranda +1

We compare the perimeter measure with the Airault-Malliavin surface measure and we prove that all open convex subsets of abstract Wiener spaces have finite perimeter. By an explici…

math.AP2010★ 1 cited

Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $R^{d}$

Alessandra Lunardi

We consider a class of second order linear nonautonomous parabolic equations in R^d with time periodic unbounded coefficients. We give sufficient conditions for the evolution opera…

math.AP2010

On the Dirichlet semigroup for Ornstein -- Uhlenbeck operators in subsets of Hilbert spaces

Giuseppe Da Prato, Alessandra Lunardi

We consider a family of self-adjoint Ornstein--Uhlenbeck operators $L_{α}$ in an infinite dimensional Hilbert space H having the same gaussian invariant measure $μ$ for all $α\in [0…

math.AP2008★ 24 cited

Asymptotic behavior and hypercontractivity in nonautonomous Ornstein-Uhlenbeck equations

Matthias Geissert, Alessandra Lunardi

In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated…

math.AP2008★ 25 cited

Invariant Measures and Maximal L^2 Regularity for Nonautonomous Ornstein-Uhlenbeck Equations

Matthias Geissert, Alessandra Lunardi

We characterize the domain of the realization of the linear parabolic operator Gu := u_t + L(t)u (where, for each real t, L(t) is an Ornstein-Uhlenbeck operator), in L^2 spaces wit…

Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension

Time regularity for generalized Mehler semigroups

Schauder theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces

Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension

On the law of the minimum of the solutions to a class of unidimensional SDEs

BV functions in Hilbert spaces

Malliavin Calculus for non Gaussian differentiable measures and surface measures in Hilbert spaces

Averaging principle for non autonomous slow-fast systems of stochastic RDEs: the almost periodic case

Strong convergence of solutions to nonautonomous Kolmogorov equations

Semilinear nonautonomous parabolic equations with unbounded coefficients in the linear part

Surface measures in infinite dimension

BV functions on convex domains in Wiener spaces

Maximal Sobolev regularity in Neumann problems for gradient systems in infinite dimensional domains

Traces of Sobolev functions on regular surfaces in infinite dimensions

Sobolev regularity for a class of second order elliptic PDE's in infinite dimension

Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

Maximal L2 regularity for Dirichlet problems in Hilbert spaces

Perimeter of sublevel sets in infinite dimensional spaces

Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in Rd

On the Dirichlet semigroup for Ornstein -- Uhlenbeck operators in subsets of Hilbert spaces

Asymptotic behavior and hypercontractivity in nonautonomous Ornstein-Uhlenbeck equations

Invariant Measures and Maximal L^2 Regularity for Nonautonomous Ornstein-Uhlenbeck Equations

Maximal $L^{2}$ regularity for Dirichlet problems in Hilbert spaces

Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $R^{d}$