Homogenization of Poisson's kernel and applications to boundary control

DOI10.1016/j.matpur.2005.12.001zbMath0617.35014OpenAlexW1981973570MaRDI QIDQ1821943

Marco Avellaneda, Fang-Hua Lin

Publication date: 1989

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2005.12.001

zbMATH Keywords

asymptotic expansionGreen's functionexact boundary controllabilityPoisson kernelshomogenized problem

Mathematics Subject Classification ID

Controllability (93B05) Asymptotic behavior of solutions to PDEs (35B40) Perturbations in context of PDEs (35B20) Stability of control systems (93D99)

Related Items

Uniform boundary controllability and homogenization of wave equations ⋮ Homogenization of elliptic systems with Neumann boundary conditions ⋮ Green's matrices and boundary estimates in parabolic homogenization ⋮ In memoriam: Marco Avellaneda (1955–2022) ⋮ Periodic homogenization of Green's functions for Stokes systems ⋮ Gaussian bounds and asymptotic expansions of Green function in parabolic homogenization ⋮ Liouville theorems and optimal regularity in elliptic equations ⋮ Hardy spaces and the Neumann problem in \(L^p\) for elliptic equation with periodic high-contrast coefficients in Lipschitz domains ⋮ Homogenization of elliptic boundary value problems in Lipschitz domains ⋮ Homogenization and concentration for a diffusion equation with large convection in a bounded domain ⋮ Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer ⋮ Homogenization of elliptic problems with Neumann boundary conditions in non-smooth domains ⋮ Improved regularity in bumpy Lipschitz domains ⋮ Exact controllability for the wave equation with variable coefficients ⋮ Layer potential methods for elliptic homogenization problems ⋮ Periodic Homogenization of Green and Neumann Functions ⋮ Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation ⋮ Uniform Lipschitz estimates in bumpy half-spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Identification and rational \(L^ 2\) approximation: A gradient algorithm
• The CF table
• Toeplitz matrix techniques and convergence of complex weight Padé approximants
• A computational algorithm to determine cracks from electrostatic boundary measurements
• Rational approximation in the real Hardy space \(H_ 2\) and Stieltjes integrals: A uniqueness theorem
• Potential techniques for boundary value problems on \(C^1\)-domains
• On the convergence of generalized Padé approximants
• A criterion for uniqueness of a critical point in \(H_ 2\) rational approximation
• Carleson curves, Muckenhoupt weights, and Toeplitz operators
• The convergence of Padé approximants to functions with branch points
• Problems of Addamjan-Arov-Krein type on subsets of the circle and minimal norm extensions
• An \(L^{p}\) analog to AAK theory for \(p\geq 2\)
• Asymptotics for minimal Blaschke products and best \(L_1\) meromorphic approximants of Markov functions.
• Inverse Dirichlet problem and conformal mapping
• Infinite Hankel matrices and generalized Caratheodory-Fejer and Riesz problems
• Crack detection using electrostatic measurements
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Existence and Generic Properties of L² Approximants for Linear Systems
• ON MARKOV'S THEOREM FOR MULTIPOINT PADÉ APPROXIMANTS
• A Uniqueness Result Concerning the Identification of a Collection of Cracks from Finitely Many Electrostatic Boundary Measurements
• On the inverse emergent plane crack problem
• How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian?
• Stable determination of a crack from boundary measurements
• Continuity of the Operator of Best Uniform Approximation by Bounded Analytic Functions
• Uniqueness and stability for the determination of boundary defects by electrostatic measurements
• Recovery of pointwise sources or small inclusions in 2D domains and rational approximation
• Identification of planar cracks by complete overdetermined data: inversion formulae
• On finding a surface crack from boundary measurements
• Determining Linear Cracks by Boundary Measurements: Lipschitz Stability
• Unique Determination of Multiple Cracks by Two Measurements
• Unique Determination of a Collection of a Finite Number of Cracks from Two Boundary Measurements
• A linear sampling method for inverse scattering from an open arc
• The 𝐻^{𝑝} spaces of an annulus
• THE DISTRIBUTION OF POLES OF RATIONAL FUNCTIONS OF BEST APPROXIMATION AND RELATED QUESTIONS
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform
• Analytic Functions of Class H p
• Asymptotic uniqueness of best rational approximants of given degree to Markov functions in \({\mathcal L}^2\) of the circle
• Best meromorphic approximation of Markov functions on the unit circle.