Stable liftings of polynomial traces on tetrahedra

Internet publication

On the reference tetrahedron K, we construct, for each k∈N0, a right inverse for the trace operator u↦(u,∂nu,…,∂knu)|∂K. The operator is stable as a mapping from the trace space of Ws,p(K) to Ws,p(K) for all p∈(1,∞) and s∈(k+1/p,∞). Moreover, if the data is the trace of a polynomial of degree N∈N0, then the resulting lifting is a polynomial of degree N. One consequence of the analysis is a novel characterization for the range of the trace operator.

Authors: Parker, C; Suli, E

• Publication status: Published
• Peer review status: Not peer reviewed
• Host title: CoRR - arXiv
• Publication date: 2024-02-24
• DOI: 10.48550/arXiv.2402.15789
• Language: English
• Keywords: polynomial lifting; trace lifting; polynomial extension