Tunneling estimates and approximate controllability for hypoelliptic equations

DOI10.1090/memo/1357zbMath1500.35002arXiv1703.10797OpenAlexW2604512536MaRDI QIDQ5063345

Matthieu Léautaud, Camille Laurent

Publication date: 17 March 2022

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.10797

zbMATH Keywords

heat equationwave equationeigenfunctionscontrol theoryhypoelliptic operatorsstability estimates

Mathematics Subject Classification ID

Controllability (93B05) Heat equation (35K05) Observability (93B07) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Wave equation (35L05) Continuation and prolongation of solutions to PDEs (35B60) Hypoelliptic equations (35H10) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

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Cites Work

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• 2\textsc{d} Grushin-type equations: minimal time and null controllable data
• Heat equation on the Heisenberg group: observability and applications
• Note on the cost of the approximate controllability for the heat equation with potential
• A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups
• Observability of heat processes by transmutation without geometric restrictions
• Stabilization of the wave equation by the boundary
• Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension
• Sharp observability estimates for heat equations
• Some controllability results for the 2D Kolmogorov equation
• The analytic embedding of abstract real-analytic manifolds
• Unicité et non unicité du problème de Cauchy pour une classe d'opérateurs différentiels à caractéristiques doubles
• On the controllability of anomalous diffusions generated by the fractional Laplacian
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• An introduction to Sobolev spaces and interpolation spaces
• Null-controllability of the Kolmogorov equation in the whole phase space
• Uniqueness for an ill-posed problem
• Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems
• Non prolongement unique des solutions d'opérateurs somme de carrés. (Unique non extension of solutions of sums of square operators)
• Nodal sets of eigenfunctions on Riemannian manifolds
• Sur l'unicité du prolongement des solutions des équations elliptiques dégénérées
• Analytic control. I: A priori estimates
• Hypoelliptic differential operators and nilpotent groups
• Unique continuation for operators with partially analytic coefficients
• Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients
• Non-null-controllability of the Grushin operator in 2D
• Quantitative unique continuation for operators with partially analytic coefficients. Application to approximate control for waves
• Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
• Morse-Sard type results in sub-Riemannian geometry
• Spectral inequality and resolvent estimate for the bi-Laplace operator
• Observability of the heat equation, geometric constants in control theory, and a conjecture of Luc Miller
• Null controllability of Kolmogorov-type equations
• Null-controllability of non-autonomous Ornstein-Uhlenbeck equations
• Null controllability of Grushin-type operators in dimension two
• The Laplace-Beltrami operator in almost-Riemannian geometry
• Hypoellipticity and loss of derivatives
• Linear differential systems with singularities and an application to transitive Lie algebras
• Hypoelliptic second order differential equations
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Un problème aux limites pour une classe d'opérateurs hypoelliptiques du second ordre. (A problem on the limits for a class of second order hypoelliptic operators)
• Uniform observability estimates for linear waves
• Spectral inequality and optimal cost of controllability for the Stokes system
• An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields
• Phase-space analysis and pseudodifferential calculus on the Heisenberg group
• Introduction to Smooth Manifolds
• Waves, damped wave and observation
• On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
• The Control Transmutation Method and the Cost of Fast Controls
• GLOBAL CARLEMAN ESTIMATES FOR DEGENERATE PARABOLIC OPERATORS WITH APPLICATIONS
• The uncertainty principle and sharp gårding inequalities
• La condition de hörmander-khon pour les operateurs pseudo-differentiels
• Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques
• A uniqueness theorem for second order hyperbolic differential equations
• Uniqueness and Nonuniqueness in the Cauchy Problem for Degenerate Elliptic Operators
• Contróle Exact De Léquation De La Chaleur
• Null-controllability of hypoelliptic quadratic differential equations
• Unique continuation for solutions to pde's; between hörmander's theorem and holmgren' theorem
• A Comprehensive Introduction to Sub-Riemannian Geometry
• A Unified Boundary Controllability Theory for Hyperbolic and Parabolic Partial Differential Equations
• Orbits of Families of Vector Fields and Integrability of Distributions
• Degenerate parabolic operators of Kolmogorov type with a geometric control condition
• Sub-Riemannian Geometry and Optimal Transport
• Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
• Contrôlabilité des Systèmes non Linéaires
• Bernstein functions. Theory and applications
• The cost of approximate controllability for heat equations: The linear case
• Approximate controllability for a 2D Grushin equation with potential having an internal singularity

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