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Carleman estimates for stratified media. (English) Zbl 1218.35238
Let \(\Omega=\Omega'\times (-H,H)\) be a cylinder in \(\mathbb R^n\), where \(\Omega'\) is a nonempty bounded set in \(\mathbb R^{n-1}\). Let \(S=\Omega'\times\{0\}\) be an interface where coefficients and functions may jump. The authors prove Carleman estimates for anisotropic elliptic and parabolic operators with discontinuities on \(S\).

MSC:
35R05 PDEs with low regular coefficients and/or low regular data
35J15 Second-order elliptic equations
35K10 Second-order parabolic equations
47F05 General theory of partial differential operators
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