Unal, C.Aydin, I.2025-03-232025-03-2320200133-38521588-273Xhttps://doi.org/10.1007/s10476-020-0014-1https://hdl.handle.net/11486/6958We define the weighted relative p(.)-capacity and discuss its properties in the space W 1,p(.). (Rn). Also, we investigate some properties of the weighted variable Sobolev capacity. It is shown that there is a relation between these two capacities. Moreover, we introduce the notion of thinness related to this newly defined relative capacity and prove an equivalence statement for this thinness.eninfo:eu-repo/semantics/openAccessweighted variable exponent Sobolev spacerelative capacitySobolev capacitythinnessArticle46114716710.1007/s10476-020-0014-12-s2.0-85079698107Q3WOS:000513344000012Q3