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M. A. Ragusa

Publications and source records attributed to M. A. Ragusa.

17 recordsLinked to original sources
arXiv2024

On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications

We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there is potential for future extensions, particularly in extending the concentration-compactness principle to anisotropic fractional order Sobolev spaces with variable exponents in bounded domains. This extension could find applications in solving the generalized fractional Brezis-Nirenberg problem.

math.AP↗
arXiv2022

Weak solvability of nonlinear elliptic equations involving variable exponents

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the $( p( m ), \, q( m ) )-$ equation and the nonlinearity is superlinear but does not fulfil the Ambrosetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a $( p( m ), \, q( m ) )$ equation that highlights the applicability of our theoretical results is also provided.

math.DG↗
arXiv2020

Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag-Leffler functions

In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral equation in terms of Mittag- Leffler functions. The existence and uniqueness results are established by using Schauder fixed point theorem and Banach fixed point theorem respectively. An example is given to illustrate the main results.

math.AP↗
arXiv2020

Energy estimates of harmonic maps between Riemannian manifolds

Let $Ω\subset {R}^n,$ $n \geq 3,$ be a bounded open set, $x=(x_1,x_2,\ldots,x_n)$ a generic point which belongs to $Ω,$ $u \colon Ω\to {R}^N ,$ $N>1,$ and $ Du=(D_αu^i)$, $D_α= \partial/\partial x_α, $ $α=1,\ldots,n,\,$ $i=1,\ldots,N .\,$ Main goal is the study of regularity of the minima of nondifferentiable functionals $$ {\cal F} \,=\, \int_ΩF(x,u,Du) dx. $$ having the integrand function different shapes of smoothness. The method is based on the use some majorizations for the functional, rather than the well known Euler equation associated to it.

math.AP↗
arXiv2020

Regularity criteria via one directional derivative of the velocity in anisotropic Lebesgue spaces to the 3D Navier-Stokes equations

In this paper, we consider the regularity criterion for 3D incompressible Navier-Stokes equations in terms of one directional derivative of the velocity in anisotropic Lebesgue spaces. More precisely, it is proved that u becomes a regular solution if the $\partial_3u$ satisfies $$\int^{T}_{0} \frac{\left\|\left\|\left\|\partial_3 u(t) \right\|_{L^p_{x_1}} \right\|_{L^q_{x_2}} \right\|^β_{L^{r}_{x_3}}} {1 + \ln\left(\|\partial_3u \left(t\right)\|_{L^2} + e\right)}dt < \infty,$$ $\text { where } \frac{2}β+\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=1 \text { and } 2 < p, q, r \leq \infty, 1-\left(\frac{1}{p}+\frac{1}{q}+\frac{1}{r}\right) \geq 0 $.

math.AP↗
arXiv2020

High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation

In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advection-dispersion equation. The proposed method is a fourth order centered difference operator in spatial directions and second order Crank-Nicolson method in temporal direction. By reviewing the consistency and stability of the method, the convergence of the proposed method is achieved. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed technique.

math.NA↗
arXiv2020

On the regularity of weak solutions of the Boussinesq equations in Besov spaces Dedicated to Enrique Zuazua on the occasion of his sixtieth birthday

The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space $\dot{B}_{\infty ,\infty }^{-1}(\mathbb{R}% ^{3})$, that, if the solution of the Boussinesq equation (\ref% {eq1.1}) below (starting with an initial data in $H^{2}$) is such that $% (\nabla u,\nabla θ)\in L^{2}\left( 0,T;\dot{B}_{\infty ,\infty }^{-1}(% \mathbb{R}^{3})\right)$, then the solution remains smooth forever after $T$. In this contribution, we prove the same result for weak solutions just by assuming the condition on the velocity $u$ and not on the temperature $θ$.

math.AP↗
arXiv2020

Study of Saharan dust influence on PM10 measures in Sicily from 2013 to 2015

Nowadays, particulate matter, especially that with small dimension as PM10, PM2.5 and PM1, is the air quality indicator most commonly associated with a number of adverse health effects. In this paper it is analyzed the impact that a natural event, such as the transport of Saharan dust, can have on increasing the particulate matter concentration in Sicily.Consulting the data of daily PM10 concentration, acquired by air quality monitoring network belonging to Agenzia Regionale Protezione Ambiente (Environmental Protection Regional Agency), it was possible to analyze the trend from 2013 to 2015. The days, in which the limit value was exceeded, were subjected to combined analysis. It was based on three models: interpretations of the air masses back trajectories, using the atmospheric model HYSPLIT (HYbrid Single Particle Lagrangian Integrated trajectory); on the calculation of the concentration on the ground and at high altitude particulate applying DREAM model (Dust REgional atmospheric model) and on the calculation of the concentration of mineral aerosols according to the atmospheric optical thickness (AOT) applying NAAPS model (Navy Aerosol Analysis and Prediction System).The daily limit value exceedances were attributed to the transport of Saharan dust events exclusively when the three models were in agreement with each other. Identifying the natural events, it was possible to quantify the contribution of the Saharan dust and consequently the reduction of the exceedances number.

physics.ao-ph↗
arXiv2020

Partial Regularity of Solutions to $\bm{p(x)}$-Laplacian PDEs with Discontinuous Coefficients

For $Ω\subseteq\mathbb{R}^{n}$ an open and bounded region we consider solutions $u\in W_{\text{loc}}^{1,p(x)}\big(Ω;\mathbb{R}^{N}\big)$, with $N>1$, of the $p(x)$-Laplacian system \begin{equation} \nabla\cdot\left(a(x)|Du|^{p(x)-2}Du\right)=0\text{, a.e. }x\inΩ,\notag \end{equation} where concerning the coefficient function $x\mapsto a(x)$ we assume only that \begin{equation} a\in W^{1,q}(Ω)\cap L^{\infty}(Ω),\notag \end{equation} where $q>1$ is essentially arbitrary. This implies that the coefficient in the PDE can be highly irregular, and yet in spite of this we still recover that \begin{equation} u\in\mathscr{C}_{\text{loc}}^{0,α}\big(Ω_0\big),\notag \end{equation} for each $0<α<1$, where $Ω_0\subseteqΩ$ is a set of full measure. Due to the variational methodology that we employ, our results apply to the more general question of the regularity of the integral functional \begin{equation} \int_Ωa(x)|Du|^{p(x)}\ dx.\notag \end{equation}

math.AP↗
arXiv2020

Mixed Morrey spaces and their applications to partial differential equations

In this paper, new classes of functions are defined. These spaces generalize Morrey spaces and give a refinement of Lebesgue spaces. Some embeddings between these new classes are also proved. Finally, the authors apply these classes of functions to obtain regularity results for solutions of partial differential equations of parabolic type.

math.AP↗
arXiv2020

A regularity criterion to the 3d Boussinesq equations

The paper deals with the regularity criterion for the weak solutions to the 3D Boussinesq equations in terms of the partial derivatives in Besov spaces. It is proved that the weak solution $(u,θ)$ becomes regular provided that $(\nabla_{h}u,\nabla_{h}θ)\in L^{\frac{8}{3}}(0,T;\dot{B}_{\infty ,\infty}^{-1}(\mathbb{R}^{3}))$ Our results improve and extend the well-known results by Fang-Qian for the Navier-Stokes equations.

math.AP↗
arXiv2020

Regularity for minimizers for functionals of double phase with variable exponents

The functionals of double phase type \[ \mathcal{H} (u):= \int \left(|Du|^{p} + a(x)|Du|^{q} \right) dx, ( q > p > 1, a(x)\geq 0) \] are introduced in the epoch-making paper by Colombo-Mingione for constants $p$ and $q$, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of $x$ and partly generalize their regularity results.

math.AP↗
arXiv2020

A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz space

In this paper, we study the regularity criterion of weak solutions to the three-dimensional (3D) MHD equations. It is proved that the solution $(u,b)$ becomes regular provided that one velocity and one current density component of the solution satisfy% \begin{equation} u_{3}\in L^{\frac{30α}{7α-45}}\left( 0,T;L^{α,\infty }\left( \mathbb{R}^{3}\right) \right) \text{ \ \ \ with \ \ }\frac{45}{7}% \leq α\leq \infty , \label{eq01} \end{equation}% and \begin{equation} j_{3}\in L^{\frac{2β}{2β-3}}\left( 0,T;L^{β,\infty }\left( \mathbb{R}^{3}\right) \right) \text{ \ \ \ with \ \ }\frac{3}{2}\leq β\leq \infty , \label{eq02} \end{equation}% which generalize some known results.

math.AP↗