Differentiability of Mappings of the Sobolev Space Wn−11 with Conditions on the Distortion Function

Сибирский математический журнал

S. K. Vodopyanov¹ 

[1] Novosibirsk State University

关键词: quasiconformal analysis;    Sobolev space;    capacity estimate;    differentiability;    Liouville theorem;   

DOI  :  10.1134/S0037446618060034

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We define two scales of the mappings that depend on two real parameters p and q, with n−1 ≤ q ≤ p < ∞, as well as a weight function θ. The case q = p = n and θ ≡ 1 yields the well-known mappings with bounded distortion. The mappings of a two-index scale are applied to solve a series of problems of global analysis and applications. The main result of the article is the a.e. differentiability of mappings of two-index scales.

【 授权许可】

CC BY