The Kato Square Root Problem on locally uniform domains
| Autor: | Moritz Egert, Sebastian Bechtel, Robert Haller-Dintelmann |
|---|---|
| Přispěvatelé: | Technische Universität Darmstadt (TU Darmstadt), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Boundary (topology) [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] functional calculus [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Dirichlet distribution symbols.namesake Square root 0103 physical sciences Neumann boundary condition FOS: Mathematics Boundary value problem 0101 mathematics Divergence (statistics) Mathematics Primary: 47A60 35J47. Secondary: 46E35 26A33 010102 general mathematics Mathematical analysis Ahlfors–David regular sets 47A60 35J57 Mathematics::Spectral Theory Functional Analysis (math.FA) Mathematics - Functional Analysis Elliptic operator locally uniform domains Kato square root problem symbols 010307 mathematical physics fractional Laplacian Laplace operator |
| Zdroj: | Advances in Mathematics Advances in Mathematics, Elsevier, 2020, 375, pp.107410. ⟨10.1016/j.aim.2020.107410⟩ |
| ISSN: | 0001-8708 1090-2082 |
| DOI: | 10.48550/arxiv.1902.03957 |
| Popis: | We obtain the Kato square root estimate for second order elliptic operators in divergence form with mixed boundary conditions on an open and possibly unbounded set in $\mathbb{R}^d$ under two simple geometric conditions: The Dirichlet boundary part is Ahlfors--David regular and a quantitative connectivity property in the spirit of locally uniform domains holds near the Neumann boundary part. This improves upon all existing results even in the case of pure Dirichlet or Neumann boundary conditions. We also treat elliptic systems with lower order terms. As a side product we establish new regularity results for the fractional powers of the Laplacian with boundary conditions in our geometric setup. Comment: Minor changes during publication process |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect