Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets

Autor: Moritz Egert, Sebastian Bechtel
Přispěvatelé: Technische Universität Darmstadt (TU Darmstadt), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Pure mathematics
Trace (linear algebra)
General Mathematics
Open set
Boundary (topology)
02 engineering and technology
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
01 natural sciences
Measure (mathematics)
Mathematics - Analysis of PDEs
2010 MSC: Primary: 46B70. Secondary: 46E35
0202 electrical engineering
electronic engineering
information engineering
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
0101 mathematics
Mathematics
Porous sets
Interpolation of Banach spaces
Smoothness (probability theory)
Applied Mathematics
010102 general mathematics
Primary: 46B70. Secondary: 46E35
Hardy's inequality
020206 networking & telecommunications
Lipschitz continuity
traces and extensions of Sobolev functions
Sobolev space
Mathematics - Classical Analysis and ODEs
measure density conditions
(fractional) Sobolev spaces
Analysis
Interpolation theory
Analysis of PDEs (math.AP)
Zdroj: Journal of Fourier Analysis and Applications
Journal of Fourier Analysis and Applications, Springer Verlag, 2019, 25 (5), pp.2733-2781. ⟨10.1007/s00041-019-09681-1⟩
ISSN: 1069-5869
1531-5851
Popis: 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.
Comment: Upload of the published version including the correction of some further typos
Databáze: OpenAIRE
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