Abstract
We study the boundary behavior of closed open discrete mappings from the Sobolev and Orlicz–Sobolev classes in ℝn, n ≥ 3. It is proved that such a mapping f can be extended by continuity to a boundary point x0 ∈ ∂ D of a domain D ⊂ ℝn whenever its inner dilatation of order α > n− 1 has a majorant from the finite mean oscillation class at the point in question. Another sufficient condition for the existence of a continuous extension is the divergence of some integral. We also prove some results on the continuous extension of such a mapping to an isolated boundary point.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
