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Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients. (English) Zbl 1033.35025
This paper deals with the strong unique continuation problem for second-order elliptic equations with nonsmooth coefficients $\sum^n_{i,j=1} \partial_i(g^{ij}(x)\partial_ju)= Vu+ W_1\nabla u+\nabla (W_2 u)\quad\text{in }\mathbb{R}^n.$ First, the authors state that the strong unique continuation result is a standard consequence of certain estimates of Carleman type. Second, they prove the Carleman estimates. Third, the authors use a perturbation argument to transfer these estimates to variable coefficient operators and more general exponential weights. Finally, the global construction of the weights, as well as the global Carleman estimates are explained.

##### MSC:
 35J15 Second-order elliptic equations 35B60 Continuation and prolongation of solutions to PDEs 35R05 PDEs with low regular coefficients and/or low regular data
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