2018/07/31 by Sebastian Bechtel, Moritz Egert
Mathematics · #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Boundary (topology) #Interpolation (computer graphics) #Lipschitz continuity #Nonlinear Partial Differential Equations #Open set #Potential theory #Smoothness #Sobolev space #TRACE (psycholinguistics) #Trace operator #math.AP #math.CA
paper · pdf · doi:10.1007/s00041-019-09681-1
published as Journal of Fourier Analysis and Applications, Springer Verlag, 2019, 25 (5), pp.2733-2781 · Upload of the published version including the correction of some further typos
openalex created_date 2018/07/19 · openalex publication_date 2019/04/12 · arxiv created 2021/02/22 · arxiv updated 2021/02/23 · openalex updated_date 2026/08/05
A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond Lipschitz regular domains. Previous results were limited to regular geometric configurations or Hilbertian Sobolev spaces. Sets with porous boundary and their characteristic multipliers on smoothness spaces play a major role in the arguments.