The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations

Authors

  • Haik Ghazaryan Russian - Armenian (Slavonic) University, Institute of Mathematics of National Academy of Armenia, Yerevan

Keywords:

Newton polyhedron, non-degenerate operator (equation), (almost) hypoelliptic operator (equation), multi -anisotropic Sobolev and Gevrey spaces

Abstract

 In the paper we investigate the role of the  Newton polyhedron $ \Re, $ which generates a multianisotropic  Sobolev space  $ W_{p}^{\Re} $ and   Gevrey space $ G^{\Re}, $   and the role of the  Newton polyhedron $ \Re ( P) $ of a polynomial $ P(\xi) $  ( of a linear differential operator  $ P ( D) $) in the behaviour of  $ P(\xi) $ at infinity and in the smoothness of solutions of the equation $  P ( D)u = f. $

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Published

2017-12-26

Issue

Vol. 9 No. 2 (2017)

Section

Articles

How to Cite

[1]
H. Ghazaryan, “The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations”, Armen.J.Math., vol. 9, no. 2, pp. 102–145, Dec. 2017, Accessed: Jan. 26, 2025. [Online]. Available: https://armjmath.sci.am/index.php/ajm/article/view/132