Carleman estimates for a subelliptic operator and unique continuation
Annales de l'Institut Fourier, Volume 44 (1994) no. 1, p. 129-166

We establish a Carleman type inequality for the subelliptic operator =Δ z +|x| 2 t 2 in n+1 , n2, where z n , t. As a consequence, we show that -+V has the strong unique continuation property at points of the degeneracy manifold {(0,t) n+1 |t} if the potential V is locally in certain L p spaces.

Nous démontrons une inéqualité du type de Carleman pour l’opérateur sous-elliptique de la forme =Δ z +|z| 2 t 2 dans n+1 avec n2, z n , et t. On en déduit que -+V possède la propriété d’unicité stricte du prolongement des solutions aux points (0,t), t, si le potentiel V appartient localement à des espaces L p particuliers.

@article{AIF_1994__44_1_129_0,
     author = {Garofalo, Nicola and Shen, Zhongwei},
     title = {Carleman estimates for a subelliptic operator and unique continuation},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {44},
     number = {1},
     year = {1994},
     pages = {129-166},
     doi = {10.5802/aif.1392},
     zbl = {0791.35017},
     mrnumber = {94m:35037},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1994__44_1_129_0}
}
Garofalo, Nicola; Shen, Zhongwei. Carleman estimates for a subelliptic operator and unique continuation. Annales de l'Institut Fourier, Volume 44 (1994) no. 1, pp. 129-166. doi : 10.5802/aif.1392. http://www.numdam.org/item/AIF_1994__44_1_129_0/

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