In this expository article, we review and improve uniform resolvent estimates for a family of operators and show how such results can be applied to the study of the high frequency Helmboltz equation by means of semi-classical measures. For the source term concentrated near a point, we provide a complete solution to determine the semi-classical measure.
@article{1620,
title = {Semi-classical measures and the Helmholtz Equation},
journal = {CUBO, A Mathematical Journal},
volume = {7},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/1620}
}
Ping Wang, Xue. Semi-classical measures and the Helmholtz Equation. CUBO, A Mathematical Journal, Tome 7 (2005) 27 p. http://gdmltest.u-ga.fr/item/1620/