ON A SOLUTIONS OF ONE CLASS OF ALMOST HYPOELLIPTIC EQUATIONS

G.H. Hakobyan

doi:10.46991/PSYU:A/2015.49.1.020

ON A SOLUTIONS OF ONE CLASS OF ALMOST HYPOELLIPTIC EQUATIONS

Authors

G.H. Hakobyan Chair of Higher Mathematics, Faculty of Physics, YSU, Armenia

DOI:

https://doi.org/10.46991/PSYU:A/2015.49.1.020

Keywords:

almost hypoelliptic operator (polynom), weighted Sobolev spaces, analyticity of solution

Abstract

We prove that if $P(D)=P(D_1,D_2)=\sum_\alpha\gamma_\alpha D_1^{\alpha_1}D_2^{\alpha_2}$ is almost hippoelliptic regular operator, then for enough small $\delta>0$, all solutions of equation $P(D)u=0$ from $L_{2,\delta}(R^2)$ are entire analytical functions.

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Published

2015-03-16

How to Cite

Hakobyan, G. (2015). ON A SOLUTIONS OF ONE CLASS OF ALMOST HYPOELLIPTIC EQUATIONS. Proceedings of the YSU A: Physical and Mathematical Sciences, 49(1 (236), 20–25. https://doi.org/10.46991/PSYU:A/2015.49.1.020