On the boundary behaviour of solutions to the Beltrami equations

On the boundary behavior of mappings with finite distortion in the plane

“…Finally, note that if a domain D in C is locally connected on its boundary, then there is a natural one-to-one correspondence between prime ends of D and boundary points of D. Thus, if D and D ′ are in addition locally connected on their boundaries in theorems of Sections 4 and 5, then f is extended to a homeomorphism of D onto D ′ . We obtained before it similar results when ∂D ′ was weakly flat which is a more strong condition than local connectivity of D ′ on its boundary, see, e.g., [24] and [25].…”

The Beltrami equations and prime ends

“…We obtained earlier similar results, when ∂D ′ is weakly flat, which is a more strong condition than that of local connectivity of D ′ on its boundary, see, e.g., [17,18].…”

“…The boundary behavior of W 1,1 loc homeomorphic solutions and the Dirichlet problem for degenerate Beltrami equations in Jordan domains have been studied, e.g., in [17][18][19]37]. Concerning the Carathéodory's theory of prime ends for the conformal mappings, we refer the reader to [4] and [5,Ch.…”

On the Theory of Prime Ends for Space Mappings

“…The theory of the boundary behavior for the lower Q-homeomorphisms developed here will find its applications, in particular, to mappings in classes of Sobolev and Orlicz-Sobolev and also to finitely bilipschitz mappings that a farreaching extension of the well-known classes of isometric and quasiisometric mappings, see, e.g., [18], [19], [24], [25], [26], [31] and [47].…”