We extend Federer's co-area formula to mappings $ f $ belonging to the Sobolev class $
W^{1, p}(\mathbb {R}^ n;\mathbb {R}^ m) $, $1\le m< n $, $ p> m $, and more generally, to …

The subject of harmonic maps is vast and has found many applications, and it would require
a very long book to cover all aspects, even superficially. Hence, we have made a choice; in …

A class of “absolutely continuous functions” ofnvariables is introduced. The absolute
continuity implies continuity, weak differentiability with gradient inLn, differentiability almost …

We obtain a global fractional Calderón-Zygmund regularity theory for the fractional Poisson
problem. More precisely, for Ω⊂ RN, N⩾ 2, a bounded domain with boundary∂ Ω of class …

We prove various generalizations of classical Sard's theorem to mappings f: M m→ N n
between manifolds in Hölder and Sobolev classes. It turns out that if f∈ C k, λ (M m, N n) …

Area and coarea formulas for the mappings of Sobolev classes with values in a metric space
Page 1 Siberian Mathematical Journal, Vol. 48, No. 4, pp. 621–628, 2007 Original Russian Text …

We construct explicit examples of Frostman-type measures concentrated on arbitrary simple
rectifiable curves\(\Gamma\subset\mathbb {R}^{2}\) of positive length. Based on such …

x: x∈ ϕ− 1 (y) χU (x) dHn (y),(1.1) она доказана для широких классов отображений ϕ:
U→ Rk, U⊂ Rn, n⩽ k, удовлетворяющих некоторым условиям регулярности. Эти классы …

Abstract We consider the Abelian Yang–Mills–Higgs functional, in the non-self dual scaling,
on a complex line bundle over a closed Riemannian manifold of dimension n≥ 3. This …

A classical theorem of Hahn [8] and Mazurkiewicz [19] states that X is a locally connected
continuum if and only if there exists a continuous surjection f:[0, 1]→ X. Since any cube [0, 1] …