Geodesic
L p -inequalities for the laplacian and unique continuation
Annales de l'Institut Fourier, Tome 31 (1981) no. 3, pp. 153-168.

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We prove an inequality of the type

∥ | x | r f ∥ L p ( R n ) ≤ c ( n , p , q , r ) ∥ | x | τ + μ Δ f ∥ L q ( R n ) .

This is then used to derive the unique continuation property for the differential inequality |Δf(x)|≤|v(x)||f(x)| under suitable local integrability assumptions on the function v.

Nous démontrons une inégalité de la forme

∥ | x | r f ∥ L p ( R n ) ≤ c ( n , p , q , r ) ∥ | x | τ + μ Δ f ∥ L q ( R n ) .

Comme applications nous obtenons la propriété de prolongement unique pour l’inégalité différentielle |Δf(x)|≤|v(x)||f(x)| si v∈L Loc p avec p>maxn 2 ,n-2).

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     author = {Amrein, W. O. and Berthier, A. M. and Georgescu, V.},
     title = {$L^p$-inequalities for the laplacian and unique continuation},
     journal = {Annales de l'Institut Fourier},
     pages = {153--168},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
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     year = {1981},
     doi = {10.5802/aif.843},
     mrnumber = {83g:35011},
     zbl = {0468.35017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.843/}
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Amrein, W. O.; Berthier, A. M.; Georgescu, V. $L^p$-inequalities for the laplacian and unique continuation. Annales de l'Institut Fourier, Tome 31 (1981) no. 3, pp. 153-168. doi : 10.5802/aif.843. http://geodesic.mathdoc.fr/articles/10.5802/aif.843/

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