For scalar elliptic transmission problems with piecewise Lipschitz coefficients, strong unique continuation holds at a C^{1,1} interface, proved via a new Carleman estimate and doubling inequality.
Carleman, Sur un probl` eme d’unicit´ e pour les syst` emes d’` equations aux d` eriv` ees partielles ` a deux variables ind´ ependentes, Ark
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Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem
For scalar elliptic transmission problems with piecewise Lipschitz coefficients, strong unique continuation holds at a C^{1,1} interface, proved via a new Carleman estimate and doubling inequality.