Abstract
The goal of this chapter is to review some applications of Carleman inequalities to various branches of Mathematics which are not covered in the previous ten chapters. Although some proofs are included, the emphasis in this chapter is to give a broad description of many different topics related to Carleman estimates.
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Notes
- 1.
In the above calculation, we may calculate \( 2{\text {Re}}\langle \xi \cdot \partial _{x} v,\bigl (\mu -(\xi \cdot x)\bigr ) v\rangle \) with a real parameter \(\mu \) that we can choose as \(\frac{1}{2}(\gamma _{\Omega }(\xi )-\gamma _{\Omega }(-\xi ))\): this improves (11.3.6) by allowing us to drop the 2 in its right-hand side.
- 2.
The uniqueness of these “Leray–Hopf solutions” is still an open problem in October 2018.
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Lerner, N. (2019). Perspectives and Developments. In: Carleman Inequalities. Grundlehren der mathematischen Wissenschaften, vol 353. Springer, Cham. https://doi.org/10.1007/978-3-030-15993-1_11
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DOI: https://doi.org/10.1007/978-3-030-15993-1_11
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