2026-06-02T02:14:17Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1224932025-07-14T23:55:51Zcom_20.500.14352_14col_20.500.14352_15

A necessary condition for Sobolev extension domains in higher dimensions Rajala, Tapio Takanen, Jyrki García Bravo, Miguel Sobolev extension Ciencias 12 Matemáticas We give a necessary condition for a domain to have a bounded extension operator from 𝐿1,𝑝(𝛺) to 𝐿1,𝑝(R𝑛) for the range 1 < 𝑝 < 2. The condition is given in terms of a power of the distance to the boundary of 𝛺 integrated along the measure theoretic boundary of a set of locally finite perimeter and its extension. This generalizes a characterizing curve condition for planar simply connected domains, and a condition for 𝑊1,1-extensions. We use the necessary condition to give a quantitative version of the curve condition. We also construct an example of an extension domain in R3 that is homeomorphic to a ball and has 3-dimensional boundary. Ministerio de Ciencia Depto. de Análisis Matemático y Matemática Aplicada Instituto de Matemática Interdisciplinar (IMI) Fac. de Ciencias Matemáticas TRUE pub 2025-07-14T10:09:29Z 2025-07-14T10:09:29Z 2024 journal article https://hdl.handle.net/20.500.14352/122493 XXXX-XXXX 10.1016/j.na.2023.113446 eng PID2022-138758NB-I00 open access application/pdf application/pdf Elsevier