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| We consider elliptic operators of even order with complex coefficients and we derive microlocal and local Carleman estimates near a boundary, under sub-ellipticity and strong Lopatinskii conditions or near an interface under sub-ellipticity and proper transmission conditions. Carleman estimates are weighted a priori estimates for the solutions of the associated elliptic problem. The weight is of exponential form, $\exp(\tau \varphi)$, where $\tau$ is meant to be taken as large as desired. Such estimates have numerous applications in unique continuation, inverse problems, and control theory. |
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