On Extraction of Smooth Solutions of a Class of Almost Hypoelliptic Equations with Constant Power
- Authors: Margaryan V.N.1, Ghazaryan H.G.2
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Affiliations:
- Russian-Armenian (Slavonic) University
- Yerevan State University
- Issue: Vol 53, No 1 (2018)
- Pages: 6-15
- Section: Differential Equations
- URL: https://journals.rcsi.science/1068-3623/article/view/228114
- DOI: https://doi.org/10.3103/S1068362318010028
- ID: 228114
Cite item
Abstract
A linear differential operator P(x, D) = P(x1,... xn, D1,..., Dn) = ∑αγα(x)Dα with coefficients γα(x) defined in En is called formally almost hypoelliptic in En if all the derivatives DνξP(x, ξ) can be estimated by P(x, ξ), and the operator P(x, D) has uniformly constant power in En. In the present paper, we prove that if P(x, D) is a formally almost hypoelliptic operator, then all solutions of equation P(x, D)u = 0, which together with some of their derivatives are square integrable with a specified exponential weight, are infinitely differentiable functions.
About the authors
V. N. Margaryan
Russian-Armenian (Slavonic) University
Author for correspondence.
Email: vachagan.margaryan@yahoo.com
Armenia, Yerevan
H. G. Ghazaryan
Yerevan State University
Email: vachagan.margaryan@yahoo.com
Armenia, Yerevan