Spectral inequality and resolvent estimate for the bi-Laplace operator

DOI10.4171/JEMS/939zbMath1439.35351arXiv1509.02098OpenAlexW2996665200MaRDI QIDQ2178247

Jérôme H. Le Rousseau, Luc Robbiano

Publication date: 7 May 2020

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02098

zbMATH Keywords

controllabilitystabilizationCarleman estimateinterpolation inequalityhigh-order operatorssemi-classical calculus

Mathematics Subject Classification ID

Controllability (93B05) Stabilization of systems by feedback (93D15) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) A priori estimates in context of PDEs (35B45) Boundary value problems for PDEs with pseudodifferential operators (35S15) Higher-order elliptic equations (35J30) Initial-boundary value problems for higher-order hyperbolic equations (35L35)

Related Items (16)

Tunneling estimates and approximate controllability for hypoelliptic equations ⋮ An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator ⋮ An Inverse Random Source Problem for the Biharmonic Wave Equation ⋮ Control of the Cauchy problem on Hilbert spaces: a global approach via symbol criteria ⋮ Strong unique continuation and global regularity estimates for nanoplates ⋮ Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations ⋮ Optimal three spheres inequality at the boundary for the Kirchhoff-Love plate's equation with Dirichlet conditions ⋮ Boundary local null-controllability of the Kuramoto-Sivashinsky equation ⋮ Unique continuation through hyperplane for higher order parabolic and Schrödinger equations ⋮ Uniform null controllability of a fourth-order parabolic equation with a transport term ⋮ Carleman commutator approach in logarithmic convexity for parabolic equations ⋮ Stabilization of the weakly coupled wave-plate system with one internal damping ⋮ Stability of an inverse source problem for the damped biharmonic plate equation ⋮ Boundary controllability of a cascade system coupling fourth- and second-order parabolic equations ⋮ Stabilization of the damped plate equation under general boundary conditions ⋮ Controllability results for stochastic coupled systems of fourth- and second-order parabolic equations

Cites Work

• Well-posedness and stabilization of an Euler-Bernoulli equation with a localized nonlinear dissipation involving the \(p\)-Laplacian
• Well-posedness and stability of a hinged plate equation with a localized nonlinear structural damping
• Carleman estimates for elliptic operators with complex coefficients. I: Boundary value problems
• Nonlinear damped partial differential equations and their uniform discretizations
• Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces
• Observation from measurable sets for parabolic analytic evolutions and applications
• Sharp \(L^p\)-Carleman estimates and unique continuation
• Limiting Carleman weights and anisotropic inverse problems
• Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation
• Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems
• Carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations
• Non-uniform stability for bounded semi-groups on Banach spaces
• Semigroups of linear operators and applications to partial differential equations
• Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
• Nodal sets of eigenfunctions on Riemannian manifolds
• Carleman's and subelliptic estimates
• Local energy decay of the wave equation in an exterior problem and without resonance in the neighborhood of the real line
• Null-controllability of a system of linear thermoelasticity
• Exact controllability of the superlinear heat equation
• Carleman estimates with a second large parameter
• Null and approximate controllability for weakly blowing up semilinear heat equations
• Null controllability of a thermoelastic plate
• Carleman estimates and unique continuation for solutions to boundary value problems
• A structurally damped plate equation with Dirichlet-Neumann boundary conditions
• Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface
• Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system
• Carleman estimates for anisotropic elliptic operators with jumps at an interface
• Internal stabilization of the plate equation in a square: the continuous and the semi-discretized problems
• The Calderón problem with partial data
• Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients
• Sharp counterexamples in unique continuation for second order elliptic equations
• The Lebeau–Robbiano inequality for the one-dimensional fourth order elliptic operator and its application
• Polynomial and Analytic Boundary Feedback Stabilization of Square Plate
• On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
• Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases
• Uniqueness in the Cauchy Problem for Partial Differential Equations
• On the Uniqueness of the Cauchy Problem.
• Pseudo-périodicité et séries de Fourier lacunaires
• Uniqueness theorems for second order elliptic differential equations
• Nodal sets of solutions of elliptic and parabolic equations
• Oscillatory Integrals and Unique Continuation for Second Order Elliptic Differential Equations
• Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress
• Uniqueness for the Characteristic Cauchy Problem and Strong Unique Continuation for Higher Order Partial Differential Inequalities
• Non-unicité pour des opérateurs différentiels à caractéristiques complexes simples
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• The weyl calculus of pseudo-differential operators
• Contróle Exact De Léquation De La Chaleur
• An inverse problem for the dynamical Lamé system with two sets of boundary data
• Analyticity of Solutions to Parabolic Evolutions and Applications
• Dispersive estimates for principally normal pseudodifferential operators
• Null-control and measurable sets
• On Carleman estimates with two large parameters
• Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves
• A smooth linear elliptic differential equation without any solution in a sphere
• Inverse problems for partial differential equations
• Uniqueness in inverse hyperbolic problems. Carleman estimate for boundary value problems
• 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

This page was built for publication: Spectral inequality and resolvent estimate for the bi-Laplace operator