Geodesic
On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations
Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 54-72

Voir la notice de l'article provenant de la source Math-Net.Ru

A linear differential operator $P(D)$ with constant coefficients is called almost hypoelliptic if all derivatives $P^{(\nu)}(\xi)$ of the characteristic polynomial $P(\xi)$ can be estimated above via $P(\xi)$. In this paper it is proved that all solutions of the equation $P(D)u=f$ where $f$ and all its derivatives are square integrable with a certain exponential weight, which are square integrable with the same weight, are also such that all their derivatives are square integrable with this weight, if and only if the operator $P(D)$ is almost hypoelliptic. 
@article{EMJ_2010_1_1_a6,
     author = {H. G. Ghazaryan and V. N. Margaryan},
     title = {On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations},
     journal = {Eurasian mathematical journal},
     pages = {54--72},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a6/}
}
TY  - JOUR
AU  - H. G. Ghazaryan
AU  - V. N. Margaryan
TI  - On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 54
EP  - 72
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a6/
LA  - en
ID  - EMJ_2010_1_1_a6
ER  - 
%0 Journal Article
%A H. G. Ghazaryan
%A V. N. Margaryan
%T On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations
%J Eurasian mathematical journal
%D 2010
%P 54-72
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a6/
%G en
%F EMJ_2010_1_1_a6
H. G. Ghazaryan; V. N. Margaryan. On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations. Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 54-72. http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a6/