L. Lorenzi

activity

20082022

most citedCarleman estimate for the Navier-Stokes equations and applications

6 citations · 22 across the 30 of their papers we have counts for

collaborators

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31 papers · 1 filter

math.AP2022

Generation of semigroups associated to strongly coupled elliptic operator in $L^{p} (R^{d}; R^{m})$

Luciana Angiuli, Luca Lorenzi, Elisabetta M. Mangino

A class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space $L^{p} (R^{d}; R^{m})$ with $p…

math.AP2021

On weakly coupled systems of partial differential equations with different diffusion terms

Davide Addona, Luca Lorenzi

We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space $C_{b} (R^{d}; R^{m})$ of bounded and continuous functions, assoc…

math.AP2021

Regularity results for non-linear Young equations and applications

Davide Addona, Luca Lorenzi, Gianmario Tessitore

In this paper we provide sufficient conditions which ensure that the non-linear equation $d y (t) = A y (t) d t + σ (y (t)) d x (t)$ , $t \in (0, T]$ , with $y (0) = ψ$ and $A$ being an unbounded operato…

math.AP2021★ 6 cited

Carleman estimate for the Navier-Stokes equations and applications

Oleg Y. Imanuvilov, Luca Lorenzi, M. Yamamoto

For linearized Navier-Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauc…

math.AP2019

Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface

Claude-Michel Brauner, Luca Lorenzi, Mingmin Zhang

In this paper we analyze the stability of the traveling wave solution for an ignition-temperature, first-order reaction model of thermo-diffusive combustion, in the case of high Le…

math.AP2018

On coupled systems of PDEs with unbounded coefficients

Luciana Angiuli, Luca Lorenzi

We study the Cauchy problem associated to parabolic systems of the form $D_{t} u = A (t) u$ in $C_{b} (R^{d}; R^{m})$ , the space o…

math.AP2018★ 1 cited

Instabilities in a combustion model with two free interfaces

Davide Addona, Claude-Michel Brauner, Luca Lorenzi +1

We study in a strip of $R^{2}$ a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respe…

math.AP2017

Invariant measures for systems of Kolmogorov equations

Davide Addona, Luciana Angiuli, Luca Lorenzi

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equati…

math.AP2017

On invariant measures associated to weakly coupled systems of Kolmogorov equations

Davide Addona, Luciana Angiuli, Luca Lorenzi

In this paper, we deal with weakly coupled elliptic systems $A$ with unbounded coefficients. We prove the existence and characterize all the systems of invari…

math.AP2017

$L^{p}$ -theory for Schrödinger systems

Markus Kunze, Luca Lorenzi, Abdallah Maichine +1

In this article we study for $p \in (1, \infty)$ the $L^{p}$ -realization of the vector-valued Schrödinger operator $L u := div (Q \nabla u) + V u$ . Using a noncommutat…

math.AP2017

On the estimates of the derivatives of solutions to nonautonomous Kolmogorov equations and their consequences

Luciana Angiuli, Luca Lorenzi

We consider evolution operators $G (t, s)$ associated to a class of nonautonomous elliptic operators with unbounded coefficients, in the space of bounded and continuous functions ove…

math.AP2016

Continuous dependence and uniqueness for lateral Cauchy problems for linear integro-differential parabolic equations

A. Lorenzi, L. Lorenzi, M. Yamamoto

Via Carleman estimates we prove uniqueness and continuous dependence results for lateral Cauchy problems for linear integro-differential parabolic equations without initial conditi…

math.AP2016

Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems

Davide Addona, Luciana Angiuli, Luca Lorenzi

We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to…

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

$L^{p}$ -estimates for parabolic systems with unbounded coefficients coupled at zero and first order

Luciana Angiuli, Luca Lorenzi, Diego Pallara

We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^{p} (R^{d}; R^{m})$ , $(d, m \geq 1)$ with $p \in [1, + \infty)$ . Sufficie…

math.AP2014★ 2 cited

Non autonomous parabolic problems with unbounded coefficients in unbounded domains

Luciana Angiuli, Luca Lorenzi

Given a class of nonautonomous elliptic operators $\A(t)$ with unbounded coefficients, defined in $\overline{I \times \Om}$ (where $I$ is a right-halfline or $I = R$ and $\Om\subset…

math.AP2014

Kernel estimates for nonautonomous Kolmogorov equations with potential term

Markus Kunze, Luca Lorenzi, Abdelaziz Rhandi

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion…

math.AP2013★ 1 cited

On the Dirichlet and Neumann evolution operators in R^d_+

Luciana Angiuli, Luca Lorenzi

We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators $G_{D} (t, s)$ and $G_{N} (t, s)$ associated with a cla…

math.AP2012

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

Claude-Michel Brauner, Lina Hu, Luca Lorenzi

We consider a free interface problem which stems from a solid-gas model in combustion with pattern formation. We derive a third-order, fully nonlinear, self-consistent equation for…

math.AP2012

Two-dimensional stability analysis in a HIV model with quadratic logistic growth term

Claude-Michel Brauner, Xinyue Fan, Luca Lorenzi

We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-d…

math.AP2012

Nonautonomous Kolmogorov equations in the whole space: a survey on recent results

Luca Lorenzi

In this paper we survey some recent results concerned with nonautonomous Kolmogorov elliptic operators. Particular attention is paid to the case of the nonautonomous Ornstein-Uhlen…

math.AP2012★ 3 cited

A strongly ill-posed problem for a degenerate parabolic equation with unbounded coefficients in an unbounded domain $Ω \times O$ of $R^{M + N}$

Alfredo Lorenzi, Luca Lorenzi

In this paper we deal with a strongly ill-posed second-order degenerate parabolic problem in the unbounded open set $Ω \times O \subset R^{M + N}$ , related to a line…

math.AP2012

On improvement of summability properties in nonautonomous Kolmogorov equations

Luciana Angiuli, Luca Lorenzi

Under suitable conditions, we obtain some characterization of supercontractivity, ultraboundedness and ultracontractivity of the evolution operator $G (t, s)$ associated to a class o…

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…

Generation of semigroups associated to strongly coupled elliptic operator in Lp(Rd;Rm)

On weakly coupled systems of partial differential equations with different diffusion terms

Regularity results for non-linear Young equations and applications

Carleman estimate for the Navier-Stokes equations and applications

Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface

On coupled systems of PDEs with unbounded coefficients

Instabilities in a combustion model with two free interfaces

Invariant measures for systems of Kolmogorov equations

On invariant measures associated to weakly coupled systems of Kolmogorov equations

Lp-theory for Schrödinger systems

On the estimates of the derivatives of solutions to nonautonomous Kolmogorov equations and their consequences

Continuous dependence and uniqueness for lateral Cauchy problems for linear integro-differential parabolic equations

Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems

Strong convergence of solutions to nonautonomous Kolmogorov equations

Lp-estimates for parabolic systems with unbounded coefficients coupled at zero and first order

Non autonomous parabolic problems with unbounded coefficients in unbounded domains

Kernel estimates for nonautonomous Kolmogorov equations with potential term

On the Dirichlet and Neumann evolution operators in R^d_+

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

Two-dimensional stability analysis in a HIV model with quadratic logistic growth term

Nonautonomous Kolmogorov equations in the whole space: a survey on recent results

A strongly ill-posed problem for a degenerate parabolic equation with unbounded coefficients in an unbounded domain Ω×O of RM+N

On improvement of summability properties in nonautonomous Kolmogorov equations

Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

Generation of semigroups associated to strongly coupled elliptic operator in $L^{p} (R^{d}; R^{m})$

$L^{p}$ -theory for Schrödinger systems

$L^{p}$ -estimates for parabolic systems with unbounded coefficients coupled at zero and first order

A strongly ill-posed problem for a degenerate parabolic equation with unbounded coefficients in an unbounded domain $Ω \times O$ of $R^{M + N}$