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Non-linear singular drifts and fractional operators: when Besov meets Morrey and Campanato
Potential analysis. 2018. Vol. 49. No. 1. P. 1–35.
Chamorro D., Menozzi S.
Within the global setting of singular drifts in Morrey-Campanato spaces presented
in Chamorro and Menozzi (Revista Matem´atica Iberoamericana 32(N◦4): 1445–1499
2016) we study now the H¨older regularity properties of the solutions of a transport-diffusion
equation with nonlinear singular drifts that satisfy a Besov stability property. We will see
how this Besov information is relevant and how it allows to improve previous results. Moreover,
in some particular cases we show that as the nonlinear drift becomes more regular, in
the sense of Morrey-Campanato spaces, the additional Besov stability property will be less
useful.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Artamonov S., Руновский К., Шмайссер Х., Математические заметки 2020 Т. 108 № 4 С. 617–621
Added: November 4, 2020
Kosov E., Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 5 P. 1249–1268
We study fractional smoothness of measures on R^k, that are images of a Gaussian measure under mappings from Gaussian Sobolev classes. As a consequence we obtain Nikolskii--Besov fractional regularity of these distributions under some weak nondegeneracy assumption. ...
Added: December 27, 2019
Kosov E., Sbornik Mathematics 2019 Vol. 210 No. 5 P. 663–692
We give an equivalent description of Besov spaces in terms of a new modulus of continuity. Then we use a similar approach to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure. ...
Added: July 11, 2019
Malinnikova E., Nikolay N. Osipov, Journal of Fourier Analysis and Applications 2019 Vol. 25 No. 3 P. 804–818
We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb Math 205(7): 1004–1023, 2014) and answering Havin’s question to one of the authors. Two versions of Rubio de Francia’s operator are discussed: it is shown that exponential factors are needed for the boundedness of the operator ...
Added: October 30, 2018
Bogachev V., Kosov E., Zelenov G., Transactions of the American Mathematical Society 2018 Vol. 370 No. 6 P. 4401–4432
We prove that the distribution density of any non-constant polynomial f(\xi _1,\xi _2,\ldots ) of degree d in independent standard Gaussian random variables \xi _i (possibly, in infinitely many variables) always belongs to the Nikolskii-Besov space B^{1/d}(R) of fractional order 1/d (and this order is best possible), and an analogous result holds for polynomial mappings ...
Added: July 20, 2018
Kosov E., Journal of Mathematical Analysis and Applications 2018 Vol. 462 No. 1 P. 390–406
We show that a measure on the real line, that is the image of a log-concave measure under a polynomial of degree d, possesses a density from the Nikolskii–Besov class of fractional order 1/d. This result is used to prove an estimate for the total variation distance between such measures in terms of the Fortet–Mourier ...
Added: July 20, 2018
Bogachev V., Kosov E., Popova S., Doklady Mathematics 2017 Vol. 96 No. 2 P. 449–453
A new characterization of Nikolskii–Besov classes via integration by parts is obtained ...
Added: November 1, 2017
Bogachev V., Zelenov G., Kosov E., Доклады Академии наук 2016 Т. 469 № 6 С. 651–655
В работе изложены результаты о принадлежности образов гауссовских мер при полиномиальных отображениях классам Никольского-Бесова. ...
Added: October 15, 2016
Kolesnikov A., Tikhonov S. Y., Calculus of Variations and Partial Differential Equations 2014 Vol. 49 No. 3-4 P. 1187–1197
Let \mu = e^{-V} \ dx be a probability measure and T = \nabla \Phi be the optimal transportation mapping pushing forward \mu onto a log-concave compactly supported measure \nu = e^{-W} \ dx. In this paper, we introduce a new approach to the regularity problem for the corresponding Monge--Amp{\`e}re equation e^{-V} = \det D^2 ...
Added: March 12, 2014