Showing papers in "Annali Dell'universita' Di Ferrara in 2016"
TL;DR: In this paper, the authors established the boundedness of the strong maximal operator on mixed-norm spaces by using extrapolation, and obtained a non-trivial boundedness result for the SMA in variable exponent analysis.
Abstract: We establish the boundedness of the strong maximal operator on mixed-norm spaces by using extrapolation. In particular, we obtain a non-trivial boundedness result for the strong maximal operator in variable exponent analysis.
31 citations
TL;DR: For bounded Lipschitz domains, this article showed that Korn's first inequality holds for vector fields satisfying homogeneous mixed tangential and normal boundary conditions, and showed that the first inequality also holds for vectors with normal boundary condition.
Abstract: We prove that for bounded Lipschitz domains in \(\mathbb {R}^{N}\) Korn’s first inequality holds for vector fields satisfying homogeneous mixed tangential and normal boundary conditions.
10 citations
TL;DR: In this article, it was shown that a prime ring R with center Z satisfies the standard identity in four variables if R admits a non-identity automorphism such that for all u in some non-central Lie ideal L of R, whenever n is a fixed positive integer.
Abstract: In the present paper it is shown that a prime ring R with center Z satisfies \(s_4\), the standard identity in four variables if R admits a non-identity automorphism \(\sigma \) such that \([u^\sigma ,u]^nu^\sigma \in Z\) for all u in some non-central Lie ideal L of R, whenever \(char(R)>n\) or \(char(R)=0\), where n is a fixed positive integer. This result is in the spirit of theorems such as Posner’s second theorem or the Herstein’s theorem on derivations with central values.
7 citations
TL;DR: In this paper, the authors studied semilinear degenerate elliptic boundary value problems arising in combustion theory that obey a general Arrhenius equation and a general Newton law of heat exchange.
Abstract: This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in combustion theory that obey a general Arrhenius equation and a general Newton law of heat exchange. Our degenerate boundary conditions include as particular cases the isothermal condition (Dirichlet condition) and the adiabatic condition (Neumann condition). We prove that ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless rate of heat production. More precisely, we give sufficient conditions for our semilinear boundary value problems to have three positive solutions, which suggests that the bifurcation curves are S-shaped.
7 citations
TL;DR: In this paper, the authors derived a Vlasov-like equation for the particle distribution function, when adopting a mean-field rescaling of the particle system, and investigated this question when the particles are subjected to friction and Brownian motion.
Abstract: We are interested in models describing the motion of particles that exchange momentum and energy with their environment, represented as a vibrating field. As the number of particles goes to \(\infty \), we derive a Vlasov-like equation for the particle distribution function, when adopting a mean-field rescaling of the particle system. We also investigate this question when, additionally, the particles are subjected to friction and Brownian motion.
7 citations
TL;DR: In this paper, a prime ring of characteristic different from 2 with Utumi quotient ring U, C is the extended centroid of R, and G and X are two nonzero generalized derivations of R and X is a multilinear polynomial over C which is not central valued on R.
Abstract: Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U, C be the extended centroid of \(R,\, F\) and G be two nonzero generalized derivations of R and \(f(x_1,\ldots ,x_n)\) be a multilinear polynomial over C which is not central valued on R. If
$$\begin{aligned} {[}F(u)u, G(v)v]=0 \end{aligned}$$
for all \(u,v\in f(R)\), then there exist \(a,b\in U\) such that \(F(x)=ax\) and \(G(x)=bx\) for all \(x\in R\) with \([a, b]=0\) and \(f(x_1,\ldots ,x_n)^2\) is central valued on R.
4 citations
TL;DR: In this article, the authors define k-multiplicatively e-perfect numbers and prove some results on them, based on ideas and results by Sandor (J Inequal pure Appl Math 2:Art. 3, 2001; J Inequal Pure Appl Math 5: 2004).
Abstract: In this article, based on ideas and results by Sandor (J Inequal Pure Appl Math 2:Art. 3, 2001; J Inequal Pure Appl Math 5, 2004), we define k-multiplicatively e-perfect numbers and k-multiplicatively e-superperfect numbers and prove some results on them. We also characterize the k-T0T∗-perfect numbers defined by Das and Saikia (Notes Number Theory Discrete Math 19:37–42, 2013) in details.
3 citations
TL;DR: It is proved that the sequence generated by the iterative algorithm converges strongly to a solution of the system of split variational inequality problems.
Abstract: In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using a projection method, we propose an iterative algorithm for solving this system of split variational inequality problems. Further, we prove that the sequence generated by the iterative algorithm converges strongly to a solution of the system of split variational inequality problems. Furthermore, we discuss some consequences of the main result. The iterative algorithms and results presented in this paper generalize, unify and improve the previously known results of this area.
3 citations
TL;DR: In this article, the generalized growth and polynomial approximation of the entire function solution of the Helmholtz equation in Smirnov spaces were studied in terms of the coefficients and approximation errors using function theoretic methods.
Abstract: In this paper, we study the generalized growth and polynomial approximation of entire function solution of Helmholtz equation in \(R^2\) in Smirnov spaces [\(\varepsilon _p (S)\) and \(\varepsilon ^{^\prime }_p(S), 1\le p\le \infty \)] where S is finitely simply connected domain in the complex plane with the boundary that belongs to the Al’per class (Izv AN SSSR Ser Matem 19(3):423–444, 1955). Some bounds on generalized order and generalized type of entire solution of Helmholtz equation have been obtained in terms of the coefficients and approximation errors using function theoretic methods. Our results extend and improve the results of Kumar (J Appl Anal 18:179–196, 2012).
2 citations
TL;DR: In this article, the Dirichlet problem for Hamilton-Jacobi equations with respect to the variable x was studied and a class of Caratheodory functions H for which the problem admits a (maximal) generalized solution which coincides with the classical viscosity solution was found.
Abstract: We study the Dirichlet problem for Hamilton–Jacobi equations of the form
$$\begin{aligned} {\left\{ \begin{array}{ll} H(x,
abla u(x)) = 0 &{}\quad \text {in} \ \Omega \\ u(x)=\varphi (x) &{}\quad \text {on} \ \partial \Omega , \end{array}\right. } \end{aligned}$$
without continuity assumptions on the hamiltonian H with respect to the variable x. We find a class of Caratheodory functions H for which the problem admits a (maximal) generalized solution which, in the continuous case, coincides with the classical viscosity solution.
2 citations
TL;DR: In this article, the authors consider the stableness of bounded linear operators in a Hilbert space and provide conditions that a linear operator is stable (Hurwitzian) if its spectrum is located in the open left half-plane.
Abstract: A linear operator is said to be stable (Hurwitzian) if its spectrum is located in the open left half-plane. We consider the following problem: let A and B be bounded linear operators in a Hilbert space, and A be stable. What are the conditions that provide the stability of \(A+B\)?
TL;DR: In this article, an injectivity criterion for the single layer potential on ellipses is given, where the injectivity is based on the single-layer potential on an ellipse.
Abstract: An injectivity criterion for the single layer potential on ellipses is given.
TL;DR: In this paper, uniqueness theorems for functions that share polynomials with higher order derivatives were proved for polynomial functions with higher-order derivatives, and they proved uniqueness theorem for entire functions that shared polynoms with higherorder derivatives.
Abstract: We prove uniqueness theorems for entire functions that share polynomials with higher order derivatives.
TL;DR: In this article, a sequence of Stancu type integral operators involving q-Beta functions is introduced, and the limit operator of their sequence of integral operators is defined, and approximate approximation theorems for it are established.
Abstract: We introduce a sequence of Stancu type integral operators involving q-Beta functions, and we establish some direct results, which include a Korovkin type theorem and error estimations in terms of the modulus of continuity and the Lipschitz type maximal function, respectively. We also define the limit operator of our sequence of operators, and we obtain quantitative approximation theorems for it.
TL;DR: In this article, it was shown that m-compatible boundaries exist for demi-normal varieties without Cartier canonical classes, and that the singularities defined in terms of these boundaries are none other than Cartier singularities.
Abstract: The birational classification of varieties inevitably leads to the study of singularities. The types of singularities that occur in this context have been studied by Mori, Kollar, Reid, and others, beginning in the 1980s with the introduction of the Minimal Model Program. Normal singularities that are terminal, canonical, log terminal, and log canonical, and their non-normal counterparts, are typically studied by using a resolution of singularities (or a semi-resolution), and finding numerical conditions that relate the canonical class of the variety to that of its resolution. In order to do this, it has been assumed that a variety X is has a $${\mathbb {Q}}$$
-Cartier canonical class: some multiple $$mK_X$$
of the canonical class is Cartier. In particular, this divisor can be pulled back under a resolution $$f: Y \rightarrow X$$
by pulling back its local sections. Then one has a relation $$K_Y \sim \frac{1}{m}f^*(mK_X) + \sum a_iE_i$$
. It is then the coefficients of the exceptional divisors $$E_i$$
that determine the type of singularities that belong to X. It might be asked whether this $${\mathbb {Q}}$$
-Cartier hypothesis is necessary in studying singularities in birational classification. de Fernex and Hacon (Compos Math 145:393–414, 2009) construct a boundary divisor $$\Delta $$
for arbitrary normal varieties, the resulting divisor $$K_X + \Delta $$
being $${\mathbb {Q}}$$
-Cartier even though $$K_X$$
itself is not. This they call (for reasons that will be made clear) an m-compatible boundary for X, and they proceed to show that the singularities defined in terms of the pair $$(X,\Delta )$$
are none other than the singularities just described, when $$K_X$$
happens to be $${\mathbb {Q}}$$
-Cartier. Thus, a wider context exists within which one can study singularities of the above types. In the present paper, we extend the results of de Fernex and Hacon (Compos Math 145:393–414, 2009) still further, to include demi-normal varieties without a $${\mathbb {Q}}$$
-Cartier canonical class. Our main result is that m-compatible boundaries exist for demi-normal varieties (Theorem 1.1). This theorem provides a link between the theory of singularities for arbitrary demi-normal varieites (whose canonical class may not $$\hbox {be } {\mathbb {Q}}$$
-Cartier), that theory being developed in the present paper, and the established theory of singularities of pairs.
TL;DR: In this article, the boundary value problem of second order singular differential equations on the whole line is considered and sufficient conditions to guarantee existence and non-existence of positive solutions are established.
Abstract: This paper is concerned with a boundary value problem of second order singular differential equations on whole line. Sufficient conditions to guarantee existence and non-existence of positive solutions are established. Our results improve some theorems in known papers but the methods used are different. We give two examples to illustrate main theorems.
TL;DR: The Dufour and Soret effect on heat and mass transfer flow of a viscous fluid in a porous medium can be described with a system of nonlinear partial differential equations.
Abstract: The Dufour and Soret effect on heat and mass transfer flow of a viscous fluid in a porous medium can be described with a system of nonlinear partial differential equations. We present various theorems of existence and uniqueness of solutions of the corresponding boundary value problems.
TL;DR: In this paper, theta-function identities for a continued fraction M(q) of Ramanujan were proved and these identities were used to prove modular identities connecting m(q and m(m(q^n) for m(n) = 2, 3, 5, and 7.
Abstract: We prove some theta-function identities for a continued fraction M(q) of Ramanujan. Then these identities are used to prove modular identities connecting M(q) and \(M(q^n)\) for \(n=\) 2, 3, 5, and 7. We also offer general theorems and reciprocity formula for the explicit evaluation of M(q).
TL;DR: In this article, the authors introduced the function representing a rapidly convergent power series which extends the well-known confluent hypergeometric function and the integral function, and obtained infinite order differential equations for which these new special functions are the eigen functions.
Abstract: In the present work, we introduce the function representing a rapidly convergent power series which extends the well-known confluent hypergeometric function \(_1F_1[z]\) as well as the integral function \( f(z) = \sum
olimits _{n=1}^\infty \frac{z^n}{n!^n} \) considered by Sikkema (Differential operators and equations, P. Noordhoff N. V., Djakarta, 1953). We introduce the corresponding differential operators and obtain infinite order differential equations, for which these new special functions are the eigen functions. First we establish some properties, as the order zero of these entire (integral) functions, integral representations, differential equations involving a kind of hyper-Bessel type operators of infinite order. Then we emphasize on the special cases, especially the corresponding analogues of the exponential, circular and hyperbolic functions, called here as \({\ell }\)-H exponential function, \({\ell }\)-H circular and \({\ell }\)-H hyperbolic functions. At the end, the graphs of these functions are plotted using the Maple software.
TL;DR: In this article, an impulsive neutral differential equation with nonlocal initial conditions in an arbitrary Banach space was considered and the existence of the mild solution was obtained by using Krasnoselskii's fixed point theorem and approximation techniques without imposing the strong restriction on nonlocal function and impulsive functions.
Abstract: This paper considers an impulsive neutral differential equation with nonlocal initial conditions in an arbitrary Banach space E. The existence of the mild solution is obtained by using Krasnoselskii’s fixed point theorem and approximation techniques without imposing the strong restriction on nonlocal function and impulsive functions. An example is also provided at the end of the paper to illustrate the abstract theory.
TL;DR: In this paper, the authors established isomorphisms for Laplace, biharmonic and Stokes operators in weighted Sobolev spaces, and provided existence and uniqueness of solutions in these weighted spaces.
Abstract: This paper establishes isomorphisms for Laplace, biharmonic and Stokes operators in weighted Sobolev spaces. The \(W^{m,p}_{\alpha }({{\mathbb {R}}}^n)\)-spaces are similar to standard Sobolev spaces \(W^{m,p}_{}({\mathbb {R}}^n)\), but they are endowed with weights \((1+|x|^2)^{\alpha /2}\) prescribing functions’ growth or decay at infinity. Although well established in \({{\mathbb {R}}}^n\) [3], these weighted results do not apply in the specific hypothesis of periodicity. This kind of problem appears when studying singularly perturbed domains (roughness, sieves, porous media, etc): when zooming on a single perturbation pattern, one often ends with a periodic problem set on an infinite strip. We present a unified framework that enables a systematic treatment of such problems in the context of periodic strips. We provide existence and uniqueness of solutions in our weighted Sobolev spaces. This gives a refined description of solution’s behavior at infinity which is of importance in the multi-scale context. The isomorphisms are valid for any relative integer m, any p in \((1,\infty )\), and any real \(\alpha \) out of a countable set of critical values for the Stokes, the biharmonic and the Laplace operators.
TL;DR: Theorem 2.1 in this article is a variant of a rigidity criterion for arbitrary singularities of Schlessinger that does not use Deformation Theory, but instead makes use of Local Grothendieck-Lefschetz Theory.
Abstract: The aim of this note is to prove, in the spirit of a rigidity result for isolated singularities of Schlessinger see Schlessinger (Invent Math 14:17–26, 1971) or also Kleiman and Landolfi (Compositio Math 23:407–434, 1971), a variant of a rigidity criterion for arbitrary singularities (Theorem 2.1 below). The proof of this result does not use Schlessinger’s Deformation Theory [Schlessinger (Trans Am Math Soc 130:208–222, 1968) and Schlessinger (Invent Math 14:17–26, 1971)]. Instead it makes use of Local Grothendieck-Lefschetz Theory, see (Grothendieck 1968, Expose 9, Proposition 1.4, page 106) and a Lemma of Zariski, see (Zariski, Am J Math 87:507–536, 1965, Lemma 4, page 526). I hope that this proof, although works only in characteristic zero, might also have some interest in its own.