Sharp L p Carleman estimates and unique continuation
Journées équations aux dérivées partielles (2003), article no. 6, 12 p.

We will present a unique continuation result for solutions of second order differential equations of real principal type P(x,D)u+V(x)u=0 with critical potential V in L n/2 (where n is the number of variables) across non-characteristic pseudo-convex hypersurfaces. To obtain unique continuation we prove L p Carleman estimates, this is achieved by constructing a parametrix for the operator conjugated by the Carleman exponential weight and investigating its L p -L p ' boundedness properties.

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     author = {David Dos Santos Ferreira},
     title = {Sharp $L^p$ {Carleman} estimates and unique continuation},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {6},
     pages = {1--12},
     publisher = {Universit\'e de Nantes},
     year = {2003},
     doi = {10.5802/jedp.620},
     zbl = {02079441},
     mrnumber = {2050592},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.620/}
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David Dos Santos Ferreira. Sharp $L^p$ Carleman estimates and unique continuation. Journées équations aux dérivées partielles (2003), article  no. 6, 12 p.. doi: 10.5802/jedp.620

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