Related papers: On Koebe's theorem for mappings with integral cons…

We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary…

Let $X, Y \subset \mathbb{R}^n$ be Lipschitz domains, and suppose there is a homeomorphism $\varphi \colon \overline{X} \to \overline{Y}$. We consider the class of Sobolev mappings $f \in W^{1,n} (X, \mathbb{R}^n)$ with a strictly positive…

We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different quasi-norms, the identification of function and sequence…

We prove that the homotopy class of a Morin mapping f: P^p --> Q^q with p-q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [DS Chess, A note on the classes [S_1^k(f)], Proc. Symp. Pure…

We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…

This manuscript is devoted to the study of mappings, satisfying the upper weighted Poletsky inequality. We study the case where the boundary of the domain may not be preserved under the mapping and, besides that, the majorant from the above…

There are investigated problems connected with local and boundary properties of Orlicz--Sobolev classes of finite distortion which are actively studied last time. It is showed that, a locally uniform limit of local homeomorphisms of…

We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces.…

We prove uniform boundedness of certain boundary representations on appropriate fractional Sobolev spaces $W^{s,p}$ with $p>1$ for arbitrary Gromov hyperbolic groups. These are closed subspaces of $L^p$ and in particular Hilbert spaces in…

Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this paper we develop an embedding theory for variable…

Interpolation inequalities play an important role in the study of PDEs and their applications. There are still some interesting open questions and problems that related to integral estimates and regularity of solutions to the elliptic…

Let $K\ge 1$ and $p\in(1,2]$. We obtain asymptotically sharp constant $c(K,p)$, when $K\to 1$ in the inequality $$\|\Im f\|_{p}\le c(K,p)\|\Re(f)\|_p$$ where $f\in \mathbf{h}^p$ is a $K-$quasiregular harmonic mapping in the unit disk…

Spectral approximation by polynomials on the unit ball is studied in the frame of the Sobolev spaces $W^{s}_p(\ball)$, $1<p<\infty$. The main results give sharp estimates on the order of approximation by polynomials in the Sobolev spaces…

Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that…

We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…

Poincar\'{e}-Sobolev-type inequalities involving rearrangement-invariant norms on the entire $\mathbb{R}^n$ are provided. Namely, inequalities of the type $\|u-P\|_{Y(\mathbb{R}^n)}\leq C\|\nabla^m u\|_{X(\mathbb{R}^n)}$, where $X$ and $Y$…

We study the log-concave measures, their characterization via the Pr\'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev…

We investigate a rearrangement inequality for pairs of n-square matrices: Let |A\|_p denote the C^p trace norm of an n-square matrix A. Consider the quantity |A+B|_p^p + |A-B|_p^p. Under certain positivity conditions, we show that this is…

Approximations of the image and integral funnel of the closed ball of the space $L_p,$ $p>1,$ under Urysohn type integral operator are considered. The closed ball of the space $L_p,$ $p>1,$ is replaced by the set consisting of a finite…

We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…