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Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 2, April 2014
- pp. 393-444
- 10.1353/ajm.2014.0014
- Article
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In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann feedback on the boundary. This extends previous results from the literature: indeed, our logarithmic decay result is obtained while the part where the feedback is applied contacts the boundary zone driven by an homogeneous Dirichlet condition.We also derive a controllability result for the heat equation with the Zaremba boundary condition.