$L^p$-inequalities for the laplacian and unique continuation

Amrein, W. O., Berthier, A. M., and Georgescu, V.. "$L^p$-inequalities for the laplacian and unique continuation." Annales de l'institut Fourier 31.3 (1981): 153-168. <http://eudml.org/doc/74502>.

@article{Amrein1981,
abstract = {We prove an inequality of the type\begin\{\}\Vert |x|^\{r\_f\}\Vert \_\{L^p(\{\bf R\}^n)\} \le c(n,p,q,r)\Vert |x|^\{\tau +\mu \} \Delta f\Vert \_\{L^q(\{\bf R\}^n)\}.\end\{\}This is then used to derive the unique continuation property for the differential inequality $|\Delta f(x)| \le |v(x)|\ |f(x)|$ under suitable local integrability assumptions on the function $v$.},
author = {Amrein, W. O., Berthier, A. M., Georgescu, V.},
journal = {Annales de l'institut Fourier},
keywords = {unique continuation properties; differential inequality; non-existence of positive eigenvalues; self-adjoint Schrödinger operators},
language = {eng},
number = {3},
pages = {153-168},
publisher = {Association des Annales de l'Institut Fourier},
title = {$L^p$-inequalities for the laplacian and unique continuation},
url = {http://eudml.org/doc/74502},
volume = {31},
year = {1981},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 3
SP - 153
EP - 168
AB - We prove an inequality of the type\begin{}\Vert |x|^{r_f}\Vert _{L^p({\bf R}^n)} \le c(n,p,q,r)\Vert |x|^{\tau +\mu } \Delta f\Vert _{L^q({\bf R}^n)}.\end{}This is then used to derive the unique continuation property for the differential inequality $|\Delta f(x)| \le |v(x)|\ |f(x)|$ under suitable local integrability assumptions on the function $v$.
LA - eng
KW - unique continuation properties; differential inequality; non-existence of positive eigenvalues; self-adjoint Schrödinger operators
UR - http://eudml.org/doc/74502
ER -