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: 2024-12-17 · 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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Originally published in Armenian Journal of Mathematics, 9(2), 2017.

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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