L -estimates for the square root of elliptic systems with mixed boundary conditions

Autor: Moritz Egert
Přispěvatelé: Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)
Rok vydání: 2018
Předmět:
Pure mathematics
mixed boundary conditions
Primary: 35J47
47D06
47A60. Secondary: 42B20
47B44
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
01 natural sciences
Domain (mathematical analysis)
Mathematics - Analysis of PDEs
Square root
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Neumann boundary condition
Elliptic systems of second order
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Order (group theory)
Boundary value problem
0101 mathematics
Calderón-Zygmund decomposition for Sobolev functions
Mathematics
Semigroup
Applied Mathematics
010102 general mathematics
H∞ functional calculus
010101 applied mathematics
Mathematics - Classical Analysis and ODEs
Bounded function
Kato square root problem
Isomorphism
Lamé system
Analysis
Analysis of PDEs (math.AP)
Zdroj: Journal of Differential Equations
Journal of Differential Equations, Elsevier, 2018, 265 (4), pp.1279-1323. ⟨10.1016/j.jde.2018.04.002⟩
Journal of Differential Equations, Elsevier, In press
ISSN: 0022-0396
1090-2732
Popis: This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions on domains beyond the Lipschitz class. If there is an associated bounded semigroup on Lp0 , then we prove that the square root extends for all p $\in$ (p0, 2) to an isomorphism between a closed subspace of W1p carrying the boundary conditions and Lp. This result is sharp and extrapolates to exponents slightly above 2. As a byproduct, we obtain an optimal p-interval for the bounded H$\infty$-calculus on Lp. Estimates depend holomorphically on the coefficients, thereby making them applicable to questions of non-autonomous maximal regularity and optimal control. For completeness we also provide a short summary on the Kato square root problem in L2 for systems with lower order terms in our setting.
Upload of the published version, including a minor correction of Proposition 8.1
Databáze: OpenAIRE
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