Abstract
In this chapter, we first study Carleman estimates for quite irregular elliptic equations whose coefficients have a jump across a smooth hypersurface, following a paper by J. Le Rousseau and N. Lerner [89]. The solutions are required to satisfy some transmission conditions, devised to avoid the occurrence of simple and double layers at the interface. The second part of this chapter, unrelated to the first, is devoted to the notion of conditional pseudo-convexity introduced in a series of papers ([64, 65]) by A. Ionescu and S. Klainerman.
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Notes
- 1.
Later, we will introduce some minimal requirements on the weight function and suggest other possible choices.
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Lerner, N. (2019). Elliptic Operators with Jumps; Conditional Pseudo-convexity. In: Carleman Inequalities. Grundlehren der mathematischen Wissenschaften, vol 353. Springer, Cham. https://doi.org/10.1007/978-3-030-15993-1_10
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DOI: https://doi.org/10.1007/978-3-030-15993-1_10
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