Embedding theorem for weighted Sobolev classes on a John domain with weights that are functions of the distance to some h-set |
| |
Authors: | A A Vasil’eva |
| |
Institution: | 1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia
|
| |
Abstract: | Let Ω be a John domain, let Γ ? ?Ω be an h-set, and let g and v be weights on Ω that are distance functions to the set Γ of special form. In the paper, sufficient conditions are obtained under which the Sobolev weighted class W p,g r (Ω) is continuously embedded in the space L q,v (Ω). Moreover, bounds for the approximation of functions in W p,g r (Ω) by polynomials of degree not exceeding r ? 1 in L q,v ( $\tilde \Omega $ ) are found, where $\tilde \Omega $ is a subdomain generated by a subtree of the tree T defining the structure of Ω. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|