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Carleman estimates for parabolic equations and applications. (English) Zbl 1194.35512
The paper presents a survey devoted to Carleman estimates for parabolic equations and applications. First, the author discusses the question – what is a Carleman estimate? Then, statements related to direct derivation of estimates for parabolic equations and global estimates are provided. A major attention in the work is paid to applications to the unique continuation and the observability inequality and applications to inverse problems. One of the main parts of the work is devoted to an overview of Carleman estimates for parabolic equations. In particular, a pointwise estimate, an estimate with second large parameter, an estimate for degenerate equations are considered in it. In the final part, an overview of results on parabolic estimates, as well as on estimates with \(x\)-independent weight functions, is given.

MSC:
35R30 Inverse problems for PDEs
35K65 Degenerate parabolic equations
35B45 A priori estimates in context of PDEs
35B60 Continuation and prolongation of solutions to PDEs
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