Sharp $L^p$ Carleman estimates and unique continuation

Dos Santos Ferreira, David

doi:10.5802/jedp.620

Sharp

L^{p}

Carleman estimates and unique continuation

Dos Santos Ferreira, David

Journées équations aux dérivées partielles (2003), article no. 6, 12 p.

Résumé

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.

MR Zbl

DOI : 10.5802/jedp.620

@article{JEDP_2003____A6_0,
     author = {Dos Santos Ferreira, David},
     title = {Sharp $L^p$ {Carleman} estimates and unique continuation},
     journal = {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},
     mrnumber = {2050592},
     zbl = {02079441},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jedp.620/}
}

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Dos Santos Ferreira, David. Sharp $L^p$ Carleman estimates and unique continuation. Journées équations aux dérivées partielles (2003), article  no. 6, 12 p. doi : 10.5802/jedp.620. http://www.numdam.org/articles/10.5802/jedp.620/

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