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Remarks on the observability for the Laplace equation. (Remarques sur l’observabilité pour l’équation de Laplace.) (French) Zbl 1076.93009
This paper concerns the Laplace equation in a bounded domain with \(C^\infty\)-class boundary. Logarithmic estimates, in the sense of John, of solutions on a part of the boundary or of the domain are established. The estimates allow one to evaluate the cost of the approximate control for an elliptic model. The proofs of the estimates are based on Carleman inequalities and on some techniques developed by L. Robbiano.

MSC:
93B07 Observability
35B45 A priori estimates in context of PDEs
35B60 Continuation and prolongation of solutions to PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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