On Unclosed Mappings with Integral Constraints

This paper investigates the class of mappings that satisfy the upper weighted Poletsky inequality. We focus on the setting where the mapping is not assumed to be boundary-preserving, and the corresponding majorant satisfies the integral-type restrictions. By imposing specific geometric constraints on the definition domain and respective cluster sets of mappings, we establish the equicontinuity of the corresponding families of mappings in the closure of a domain.