Armenian Journal of Mathematics, 9(2)
2017; 102–145
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The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations

Haik Ghazaryan*

Received: 2024-12-18 · Published: 2017-12-26

© 2017 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations
Author
Haik Ghazaryan
Source journal
Armenian Journal of Mathematics, 9(2)
Published
2017-12-26
Licence
Creative Commons Attribution 4.0 International
Original
https://armjmath.sci.am/index.php/ajm/article/view/132

Abstract

In the paper we investigate the role of the  Newton polyhedron R,ℜ, which generates a multianisotropic  Sobolev space  WRpWpℜ and   Gevrey space GR,Gℜ,   and the role of the  Newton polyhedron R(P)ℜ(P) of a polynomial P(ξ)P(ξ)  ( of a linear differential operator  P(D)P(D)) in the behaviour of  P(ξ)P(ξ) at infinity and in the smoothness of solutions of the equation P(D)u=f.
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