Matrix \(\mathcal A_p\) weights, degenerate Sobolev spaces, and mappings of finite distortion. (English) Zbl 1357.30015
The authors consider degenerate Sobolev spaces where the degeneracy is controlled by matrix \(A_p\)-weights. They prove the classical Meyers-Serrin result \( H=W \) in this setting and give applications to weak solutions of degenerate \(p\)-Laplace equations and to mappings of finite distortion.
Reviewer: Matti Vuorinen (Turku)
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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