arXiv subjects

Antonio Agresti

Publications and source records attributed to Antonio Agresti.

At least 37 records · Page 2Linked to original sources

arXiv2024

The critical variational setting for stochastic evolution equations

In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. In addition, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equation, tamed Navier-Stokes equations, and Allen-Cahn equation.

math.PR↗

arXiv2024

The primitive equations with rough transport noise: Global well-posedness and regularity

In this paper we establish global well-posedness and instantaneous regularization results for the primitive equations with transport noise of Hölder regularity $ γ>\frac{1}{2}$. It is known that if $γ<1$, then the noise is too rough for a strong formulation of primitive equations in an $L^2$-based setting. To handle rough noise, we crucially use $L^q$-techniques with $q> 2$. Interestingly, we identify a family of critical anisotropic Besov spaces for primitive equations, which is new even in the deterministic case. The behavior of these spaces reflects the intrinsic anisotropy of the primitive equations and plays an essential role in establishing global well-posedness and regularization. Our results cover Kraichnan's type noise with correlation greater than one, and as a by-product, a 2D noise reproducing the Kolmogorov spectrum of turbulence. Moreover, the instantaneous regularization is new also in the widely studied case of $H^1$-data and $γ>1 $.

math.AP↗

arXiv2023

Stochastic maximal $L^p(L^q)$-regularity for second order systems with periodic boundary conditions

In this paper we consider an SPDE where the leading term is a second order operator with periodic boundary conditions, coefficients which are measurable in $(t,ω)$, and Hölder continuous in space. Assuming stochastic parabolicity conditions, we prove $L^p((0,T)\times Ω, t^κ\, \mathrm{d} t;H^{σ,q}(\mathbb{T}^d))$-estimates. The main novelty is that we do not require $p=q$. Moreover, we allow arbitrary $σ\in \mathbb{R}$ and weights in time. Such mixed regularity estimates play a crucial role in applications to nonlinear SPDEs which is clear from our previous work. To prove our main results we develop a general perturbation theory for SPDEs. Moreover, we prove a new result on pointwise multiplication in spaces with fractional smoothness.

math.PR↗

arXiv2023

Stochastic Navier-Stokes equations for turbulent flows in critical spaces

In this paper we study the stochastic Navier-Stokes equations on the $d$-dimensional torus with transport noise, which arise in the study of turbulent flows. Under very weak smoothness assumptions on the data we prove local well-posedness in the critical case $\mathbb{B}^{d/q-1}_{q,p}$ for $q\in [2,2d)$ and $p$ large enough. Moreover, we obtain new regularization results for solutions, and new blow-up criteria which can be seen as a stochastic version of the Serrin blow-up criteria. The latter is used to prove global well-posedness with high probability for small initial data in critical spaces in any dimensions $d\geq 2$. Moreover, for $d=2$, we obtain new global well-posedness results and regularization phenomena which unify and extend several earlier results.

math.AP↗

arXiv2023

Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations

This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for sufficiently noise intensity and spectrum, the blow-up of strong solutions is delayed and an enhanced diffusion effect is also established. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the $L^p(L^q)$-approach to stochastic PDEs, highlighting new connections between the two areas.

math.AP↗

arXiv2023

Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications

Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix} A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part with $\mathsf{D}(\mathcal{A})=\mathsf{D}(A)\times \mathsf{D}(D)$ though with possibly large relative bound. For such operators the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.

math.FA↗

arXiv2023

Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity

In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions -- even in case of non-smooth initial data. Crucial tools are $L^p(L^q)$-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work (Agresti and Veraar: Global existence ... ), the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.

math.AP↗

arXiv2022

The stochastic primitive equations with transport noise and turbulent pressure

In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal $L^2$-regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.

math.AP↗

arXiv2022

On the trace embedding and its applications to evolution equations

In this paper we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equation, where uniform trace estimates on the half-line are shown.

math.AP↗

arXiv2022

Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence

In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local existence and well-posedness. A second part in preparation is on blow-up criteria and regularization. Our theory is formulated in an $L^p$-setting, and because of this we can deal with nonlinearities in a very efficient way. Applications to several concrete problems and their quasilinear variants are given. This includes Burger's equation, the Allen-Cahn equation, the Cahn-Hilliard equation, reaction-diffusion equations, and the porous media equation. The interplay of the nonlinearities and the critical spaces of initial data leads to new results and insights for these SPDEs. The proofs are based on recent developments in maximal regularity theory for the linearized problem for deterministic and stochastic evolution equations. In particular, our theory can be seen as a stochastic version of the theory of critical spaces due to Prüss-Simonett-Wilke (2018). Sharp weighted time-regularity allow us to deal with rough initial values and obtain instantaneous regularization results. The abstract well-posedness results are obtained by a combination of several sophisticated splitting and truncation arguments.

math.FA↗

arXiv2022

Nonlinear parabolic stochastic evolution equations in critical spaces Part II. Blow-up criteria and instantaneous regularization

This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth, and rough initial values from critical spaces. In the first main result we obtain several new blow-up criteria for quasi- and semilinear stochastic evolution equations. In particular, for semilinear equations we obtain a Serrin type blow-up criterium, which extends a recent result of Prüss-Simonett-Wilke (2018) to the stochastic setting. Blow-up criteria can be used to prove global well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights in time play a central role in the proofs. Our second contribution is a new method to bootstrap Sobolev and Hölder regularity in time and space, which does not require smoothness of the initial data. The blow-up criteria are at the basis of these new methods. Moreover, in applications the bootstrap results can be combined with our blow-up criteria, to obtain efficient ways to prove global existence. This gives new results even in classical $L^2$-settings, which we illustrate for a concrete SPDE. In future works in preparation we apply the results of the current paper to obtain global well-posedness results, and regularity for several concrete SPDEs. These include stochastic Navier-Stokes, reaction diffusion equations, and Allen-Cahn equations. Our setting allows to put these SPDEs into a more flexible framework, where less restrictions on the nonlinearities are needed, and we are able to treat rough initial values from critical spaces. Moreover, we will obtain higher order regularity results.

math.FA↗

arXiv2021

Solution-processed two-dimensional materials for next-generation photovoltaics

In the ever-increasing energy demand scenario, the development of novel photovoltaic (PV) technologies is considered to be one of the key solutions to fulfil the energy request. In this context, graphene and related two-dimensional (2D) materials (GRMs), including nonlayered 2D materials and 2D perovskites, as well as their hybrid systems, are emerging as promising candidates to drive innovation in PV technologies. The mechanical, thermal, and optoelectronic properties of GRMs can be exploited in different active components of solar cells to design next-generation devices. These components include front (transparent) and back conductive electrodes, charge transporting layers, and interconnecting-recombination layers, as well as photoactive layers. The production and processing of GRMs in the liquid phase, coupled with the ability to on-demand tune their optoelectronic properties exploiting wet-chemical functionalization, enable their effective integration in advanced PV devices through scalable, reliable, and inexpensive printing-coating processes. Herein, we review the progresses in the use of solution-processed 2D materials in organic solar cells, dye-sensitized solar cells, perovskite solar cells, quantum dot solar cells, and organic-inorganic hybrid solar cells, as well as in tandem systems. We first provide a brief introduction on the properties of 2D materials and their production methods by solution-processing routes. Then, we discuss the functionality of 2D materials for electrodes, photoactive layer components-additives, charge transporting layers, and interconnecting layers through figures of merit, which allow the performance of solar cells to be determined and compared with the state-of-the-art values. We finally outline the roadmap for the further exploitation of solution-processed 2D materials to boost the performance of PV devices.

physics.app-ph↗

arXiv2020

Photoluminescence of MAPbI$_3$: a semiconductor science and technology point of view

In this work, we perform steady-state continuous wave (cw) photoluminescence (PL) measurements on a MAPbI$_3$ thin film in the temperature range of 10-160 K, using excitation densities spanning over almost seven orders of magnitude, in particular investigating very low densities, rarely used in the published literature. The temperature range used in this study is below or at the edge of the orthorhombic-tetragonal phase transition in MAPbI$_3$. In particular, we show that even in high quality MAPbI$_3$, capable of providing high photovoltaic efficiency, the defect density is high enough to give rise to an energy level band. Furthermore, we show that the intensity ratio between the two PL components related to the two crystalline phases, is a function of temperature and excitation. At high excitation intensities, we show that amplified spontaneous emission is attainable even in cw conditions. Time-resolved PL is also performed to justify some assignments of the PL features. Finally, our systematic approach, typical for the characterization of semiconductors, suggests that it should also be applied to hybrid halide perovskites and that, under suitable conditions, the PL characteristics of MAPbI$_3$ can be reconciled with those of conventional inorganic semiconductors.

physics.app-ph↗

arXiv2020

Time memory effect in entropy decay of Ornstein-Uhlenbeck operators

We investigate the effect of memory terms on the entropy decay of the solutions to equations with Ornstein-Uhlenbeck operators. Our assumptions on the memory kernels include Caputo-Fabrizio operators and, more generally, the stretched exponential functions. We establish a sharp rate decay for the entropy. Examples and numerical simulations are also given to illustrate the results.

math.AP↗

arXiv2019

Alternating and variable controls for the wave equation

The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which takes into account only the location in time of the observation. To this end we use Fourier series. Then we investigate the two specific cases of single exchange of the control position, and of exchange at a constant rate. In the multi-dimensional case, we analyse sufficient conditions for the exact observability relying on the multiplier method. In the last section, the multi-dimensional results are applied to specific settings and some connections between the one and multi-dimensional case are discussed; furthermore some open problems are presented.

math.OC↗

arXiv2019

MoS2 Quantum Dot/Graphene Hybrids for Advanced Interface Engineering of CH3NH3PbI3 Perovskite Solar Cell with Efficiency over 20%

Interface engineering of organic-inorganic halide perovskite solar cells (PSCs) plays a pivotal role in achieving high power conversion efficiency (PCE). Graphene and related two-dimensional materials (GRMs) are promising candidates to tune on demand the interface properties of PSCs. In this work, we fully exploit the potential of GRMs by controlling the optoelectronic properties of hybrids between molybdenum disulfide (MoS2) and reduced graphene oxide (RGO) as hole transport layer (HTL) and active buffer layer (ABL) in mesoscopic methylammonium lead iodide (CH3NH3PbI3) perovskite (MAPbI3)-based PSC. We show that zero-dimensional MoS2 quantum dots (MoS2 QDs), derived by liquid phase exfoliated MoS2 flakes, provide both hole-extraction and electron-blocking properties. In fact, on the one hand, intrinsic n-type doping-induced intra-band gap states effectively extract the holes through an electron injection mechanism. On the other hand, quantum confinement effects increase the optical band gap of MoS2 (from 1.4 eV for the flakes to > 3.2 for QDs), raising the minimum energy of its conduction band (from -4.3 eV for the flakes to -2.2 eV for QDs) above the one of conduction band of MAPbI3 (between -3.7 and -4 eV) and hindering electron collection. The van der Waals hybridization of MoS2 QDs with functionalized reduced graphene oxide (f-RGO), obtained by chemical silanization-induced linkage between RGO and (3-mercaptopropyl)trimethoxysilane, is effective to homogenize the deposition of HTLs or ABLs onto the perovskite film, since the two-dimensional (2D) nature of RGO effectively plug the pinholes of the MoS2 QDs films. Our graphene interface engineering (GIE) strategy based on van der Waals MoS2 QD/graphene hybrids enable MAPbI3-based PSCs to achieve PCE up to 20.12% (average PCE of 18.8%).

physics.app-ph↗

arXiv2019

Stability properties of stochastic maximal $L^p$-regularity

In this paper we consider $L^p$-regularity estimates for solutions to stochastic evolution equations, which is called stochastic maximal $L^p$-regularity. Our aim is to find a theory which is analogously to Dore's theory for deterministic evolution equations. He has shown that maximal $L^p$-regularity is independent of the length of the time interval, implies analyticity and exponential stability of the semigroup, is stable under perturbation and many more properties. We show that the stochastic versions of these results hold.

math.FA↗

arXiv2018

Variable Support Control for the Wave Equation: A Multiplier Approach

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof of the observability inequality, which is proven by a multiplier method. Besides our main results, we present some applications.

math.OC↗