Representation and uniqueness for boundary value elliptic problems via first order systems
| Autor: | Pascal Auscher, Mihalis Mourgoglou |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut des Hautes Etudes Scientifiques (IHES), IHES, ANR-12-BS01-0013,HAB,Aux frontières de l'analyse Harmonique(2012) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Dirichlet and Neumann problems Trace (linear algebra) Hardy spaces associated to operators General Mathematics extrapolation Boundary (topology) second order elliptic systems [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Dirichlet distribution tent spaces symbols.namesake Mathematics - Analysis of PDEs First order elliptic systems 35J25 35J57 35J46 35J47 42B25 42B30 42B35 47D06 Classical Analysis and ODEs (math.CA) FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Uniqueness Boundary value problem 0101 mathematics Representation (mathematics) \textit{a priori} estimates Mathematics 010102 general mathematics non-tangential maximal functions Half-space Hardy space boundary layer operators Functional Analysis (math.FA) Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs symbols Analysis of PDEs (math.AP) |
| Zdroj: | Revista Matemática Iberoamericana Revista Matemática Iberoamericana, European Mathematical Society, 2019, 35 (1), pp.242-315. ⟨10.4171/rmi/1054⟩ |
| ISSN: | 0213-2230 |
| DOI: | 10.4171/rmi/1054⟩ |
| Popis: | Given any elliptic system with $t$-independent coefficients in the upper-half space, we obtain representation and trace for the conormal gradient of solutions in the natural classes for the boundary value problems of Dirichlet and Neumann types with area integral control or non-tangential maximal control. The trace spaces are obtained in a natural range of boundary spaces which is parametrized by properties of some Hardy spaces. This implies a complete picture of uniqueness vs solvability and well-posedness. Comment: submitted, 70 pages. A number of maths typos have been eliminated |
| Databáze: | OpenAIRE |
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