Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with
smooth boundary, are not only of considerable intrinsic interest but have for many years …

In the present paper we study embedding operators for weighted Sobolev spaces whose
weights satisfy the well-known Muckenhoupt $ A_p $-condition. Sufficient conditions for …

SK Vodop'yanov, AD-O. Ukhlov, “Sobolev spaces and $(P,Q)$-quasiconformal mappings of
Carnot groups”, Sibirsk. Mat. Zh., 39:4 (1998), 776–795; Siberian Math. J., 39:4 (1998), 665–682 …

Composition Operators on Sobolev Spaces and Q-Homeomorphisms | Computational
Methods and Function Theory Skip to main content SpringerLink Account Menu Find a …

In 1961 G. Polya published a paper about the eigenvalues of vibrating membranes. The
“free vibrating membrane” corresponds to the Neumann–Laplace operator in bounded …

In this paper we prove discreteness of the spectrum of the Neumann–Laplacian (the free
membrane problem) in a large class of non-convex space domains. The lower estimates of …

We study mappings with bounded (p, q)-distortion associated to Sobolev spaces on Carnot
groups. Mappings of such type have applications to the Sobolev type embedding theory and …

We study generalizations of the quasiconformal homeomorphisms (the so-called
homeomorphisms with bounded (p, q)-distortion) that induce bounded composition …

In the article we study the Neumann (p, q)-eigenvalue problems in bounded Hölder γ-
singular domains Ω γ⊂ R n. In the case 1< p<∞ and 1< q< p γ∗ we prove solvability of this …

In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate
p-Laplace operator, p> 2 p> 2, in a large class of non-convex domains. This study is based …