Unique continuation for the solutions of the laplacian plus a drift
Ruiz, Alberto ; Vega, Luis
Annales de l'Institut Fourier, Tome 41 (1991), p. 651-663 / Harvested from Numdam
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Nous prouvons l’unicité du prolongement pour les solutions de l’inégalité |Δu(x)|≤V(x)|∇u(x)|, x∈Ω où Ω est une partie connexe de R n et V appartient aux espaces de Morrey F α,p , avec p≥(n-2)/2(1-α) et α<1. Ces espaces contiennent L q pour q≥(3n-2)/2 (voir L. Hörmander, Comm. PDE, 8 (1983, 21-64 et Barceló, Kenig, Ruiz, Sogge, Ill. J. of Math., 32-2 (1988), 230-245).

We prove unique continuation for solutions of the inequality |Δu(x)|≤V(x)|∇u(x)|, x∈Ω a connected set contained in R n and V is in the Morrey spaces F α,p , with p≥(n-2)/2(1-α) and α<1. These spaces include L q for q≥(3n-2)/2 (see [H], [BKRS]). If p=(n-2)/2(1-α), the extra assumption of V being small enough is needed.

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     author = {Ruiz, Alberto and Vega, Luis},
     title = {Unique continuation for the solutions of the laplacian plus a drift},
     journal = {Annales de l'Institut Fourier},
     volume = {41},
     year = {1991},
     pages = {651-663},
     doi = {10.5802/aif.1268},
     mrnumber = {92k:35043},
     zbl = {0772.35008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1991__41_3_651_0}
}

Ruiz, Alberto; Vega, Luis. Unique continuation for the solutions of the laplacian plus a drift. Annales de l'Institut Fourier, Tome 41 (1991) pp. 651-663. doi : 10.5802/aif.1268. http://gdmltest.u-ga.fr/item/AIF_1991__41_3_651_0/

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