ON THE COMPACTNESS OF ONE CLASS OF QUASICONFORMAL MAPPINGS

Abstract

We consider an elliptic system in the disk |z| < 1 for the so-called p-analytic functions. This system admits degeneration at the boundary of the disk. We prove compactness of the family of K-quasiconformal mappings, which are the solutions of the uniformly elliptic systems approximating the degenerating one.

Keywords

• quasi-conformal mappings
• sobolev spaces
• elliptic systems
• embedding theorems
• topological mappings
• dirichlet integral
• douglas integral
• harmonic functions