TY - JOUR

T1 - Basics of the Quasiconformal Analysis of a Two-Index Scale of Spatial Mappings

AU - Vodopyanov, S. K.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - We define a scale of mappings that depends on two real parameters p and q, n−1 ≤ q ≤ p < ∞ and a weight function θ. In the case of q = p = n, θ ≡ 1, we obtain the well-known mappings with bounded distortion. Mappings of a two-index scale inherit many properties of mappings with bounded distortion. They are used for solving a few problems of global analysis and applied problems.

AB - We define a scale of mappings that depends on two real parameters p and q, n−1 ≤ q ≤ p < ∞ and a weight function θ. In the case of q = p = n, θ ≡ 1, we obtain the well-known mappings with bounded distortion. Mappings of a two-index scale inherit many properties of mappings with bounded distortion. They are used for solving a few problems of global analysis and applied problems.

KW - capacity estimate

KW - quasiconformal analysis

KW - Sobolev space

KW - theorem on removable singularities

UR - http://www.scopus.com/inward/record.url?scp=85057505463&partnerID=8YFLogxK

U2 - 10.1134/S0037446618050075

DO - 10.1134/S0037446618050075

M3 - Article

VL - 59

SP - 805

EP - 834

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -