On Solvability of Regular Hypoelliptic Equations in ℝ  n

G. A. Karapetyan; H. A. Petrosyan

doi:10.3103/S1068362318040015

On Solvability of Regular Hypoelliptic Equations in ℝⁿ

Authors: Karapetyan G.A.¹, Petrosyan H.A.¹
Affiliations:
1. Russian–Armenian (Slavonic) University
Issue: Vol 53, No 4 (2018)
Pages: 187-200
Section: Functional Analysis
URL: https://journals.rcsi.science/1068-3623/article/view/228191
DOI: https://doi.org/10.3103/S1068362318040015
ID: 228191

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Abstract
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Abstract

In this paper the unique solvability of regular hypoelliptic equations in multianisotropic weighted functional spaces is proved by means of special integral representation of functions through a regular operator. The existence of the solutions is proved by constructing approximate solutions using multianisotropic integral operators.

Keywords

Multianisotropic space, hypoelliptic equation, integral representation, fundamental family of operators

About the authors

G. A. Karapetyan

Russian–Armenian (Slavonic) University

Author for correspondence.
Email: garnik_karapetyan@yahoo.com
Armenia, Yerevan

H. A. Petrosyan