Eurasian Mathematical Journal

Order-sharp estimates for decreasing rearrangements of convolutions

Elza Bakhtigareeva, Mikhail Goldman — Thu, 30 Jan 2025 00:00:00 +0000

In this paper, we study estimates for convolutions on some classes of measurable, positive and radial symmetrical functions. On this base we prove then order-sharp estimates for decreasing and symmetrical rearrangements of convolutions and for weighted mean values of rearrangements. These estimates give, in particular, a reversal of the well-known inequalities for convolutions proved by R. O’Neil.

On direct and inverse problems for systems of odd-order quasilinear evolution equations

Oleg Balashov, Andrei Faminskii — Thu, 30 Jan 2025 00:00:00 +0000

Direct and inverse initial-boundary problems on a bounded interval for systems of odd-order quasilinear evolution equations with general nonlinearities are considered. In the case of inverse problems, conditions of integral overdetermination are introduced, and right-hand sides of equations of special types are chosen as controls. Results on well-posedness of such problems are established. Assumptions on smallness of the input data or smallness of a time interval are required.

New weighted Hardy-type inequalities for monotone functions

Aigerim Kalybay, Ainur Temirkhanova — Thu, 30 Jan 2025 00:00:00 +0000

The famous Hardy inequality was formulated in 1920 and finally proved in 1925. Since then, this inequality has been greatly developed. The first development was related to the consideration of more general weights. The next step was to use more general operators with different kernels instead of the Hardy operator. At present, there are many works devoted to Hardy-type inequalities with iterated operators. Motivated by important applications, all these generalizations of the Hardy inequality are studied not only on the cone of non-negative functions but also on the cone of monotone non-negative functions. In this paper, new Hardy-type inequalities are proved for operators with kernels that satisfy less restrictive conditions than those considered earlier. The presented inequalities have already been characterized for non-negative functions. In this paper, we continue this study but for monotone non-negative functions

A discrete model of a transmission line and the Faber polynomials

Vitalii Kurbatov — Thu, 30 Jan 2025 00:00:00 +0000

The spectrum of the matrix coefficient A corresponding to a discrete model of a transmission line often has the shape of a cross. The paper suggests to use the Faber series instead of the Taylor series when calculating the matrix exponential of A. This method can enlarge the accuracy and speed up calculations

Weak continuity of Jacobians of \( W_{loc}^{1,1} \)- homeomorphisms on Carnot groups

Stepan Pavlov, Sergey Vodop’yanov — Thu, 30 Jan 2025 00:00:00 +0000

The limit of a locally uniformly converging sequence of analytic functions is an analytic function. Yu.G. Reshetnyak obtained a natural generalization of that in the theory of mappings with bounded distortion: the limit of every locally uniformly converging sequence of mappings with bounded distortion is a mapping with bounded distortion, and established the weak continuity ofthe Jacobians.

In this article, similar problems are studied for a sequence of Sobolev-class homeomorphisms defined on a domain in a two-step Carnot group. We show that if such a sequence converges to some homeomorphism locally uniformly, the sequence of horizontal differentials of its terms is bounded in \( L_{\nu,loc} \), and the Jacobians of the terms of the sequence are nonnegative almost everywhere, then thesequence of Jacobians converges to the Jacobian of the limit homeomorphism weakly in \( L_{1,loc} \); here \( \nu \) is the Hausdorff dimension of the group.

The 15th Congress of the International Society for Analysis, its Applications and Computation (ISAAC), Second Information Letter

Durvudkhan Suragan, Bolys Sabitbek — Mon, 30 Dec 2024 00:00:00 +0000

Dear Colleagues,

We are pleased to share the second information letter for the upcoming 15th International ISAAC Congress, which will take place from July 21 to 25, 2025, at the Nazarbayev University, Astana, Kazakhstan. Below you will find important updates and additional details to help you plan your participation.