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Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces. (English) Zbl 1218.35054
The authors consider a parabolic operator \(P=\partial_t-\nabla_x\delta(t,x)\nabla_x\) in \((0,T)\times \Omega\), \(\Omega\) being an open subset of \(\mathbb R^n\), \(n\geq2\), and \(\delta(t,x)\) a piecewise smooth in space yet discontinuous across a smooth interface \(S\). For this operator they prove a global in time, local in space Carleman estimate for \(P\) in the neighborhood of any point of the interface. A global in time and space Carleman estimate on \((0,T)\times M\), \(M\) a manifold, is also derived from the local result.

MSC:
35B45 A priori estimates in context of PDEs
35K10 Second-order parabolic equations
35R05 PDEs with low regular coefficients and/or low regular data
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