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Carleman estimate for a general second-order hyperbolic equation. (English) Zbl 1443.35189

Cheng, Jin (ed.) et al., Inverse problems and related topics. Extended versions of papers based on the international conference on inverse problems, Shanghai, China, October 12–14, 2018. In honor of Masahiro Yamamoto on the occasion of his 60th anniversary. Singapore: Springer. Springer Proc. Math. Stat. 310, 149-165 (2020).
Summary: In this article, we consider a general second-order hyperbolic equation. We first establish a modified Carleman estimate for this equation by adding some functions of adjustment. Then general conditions imposed on the principal parts, mixed with the weight function and the functions of adjustment are derived. Finally, we give the realizations of the weight functions by choosing suitable adjustments such that the above general conditions are satisfied in some specific cases.
For the entire collection see [Zbl 1442.35004].

MSC:

35R30 Inverse problems for PDEs
35B45 A priori estimates in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
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