We prove an inequality of the type
This is then used to derive the unique continuation property for the differential inequality under suitable local integrability assumptions on the function .
Nous démontrons une inégalité de la forme
Comme applications nous obtenons la propriété de prolongement unique pour l’inégalité différentielle si avec .
@article{AIF_1981__31_3_153_0, 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}, number = {3}, year = {1981}, doi = {10.5802/aif.843}, mrnumber = {83g:35011}, zbl = {0468.35017}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.843/} }
TY - JOUR AU - Amrein, W. O. AU - Berthier, A. M. AU - Georgescu, V. TI - $L^p$-inequalities for the laplacian and unique continuation JO - Annales de l'Institut Fourier PY - 1981 SP - 153 EP - 168 VL - 31 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.843/ DO - 10.5802/aif.843 LA - en ID - AIF_1981__31_3_153_0 ER -
%0 Journal Article %A Amrein, W. O. %A Berthier, A. M. %A Georgescu, V. %T $L^p$-inequalities for the laplacian and unique continuation %J Annales de l'Institut Fourier %D 1981 %P 153-168 %V 31 %N 3 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.843/ %R 10.5802/aif.843 %G en %F AIF_1981__31_3_153_0
Amrein, W. O.; Berthier, A. M.; Georgescu, V. $L^p$-inequalities for the laplacian and unique continuation. Annales de l'Institut Fourier, Volume 31 (1981) no. 3, pp. 153-168. doi : 10.5802/aif.843. http://archive.numdam.org/articles/10.5802/aif.843/
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