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

Ghazaryan, Hayk (2017) The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations. Armenian Journal of Mathematics, 9 (2). pp. 102-145. ISSN 1829-1163

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## 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 behavior of $P(\xi)$ at infinity and in the smoothness of solutions of the equation $P (D)u = f.$ The paper is partly of an overview nature. However, some of the results are new and not published anywhere (see, for instance, theorems 2.4, 2.5 and 4.2). Some results are proved in a new way (see, for instance, theorems 3.1, 4.3 and others).

Item Type: Article 12-xx Field theory and polynomials 798 Professor Anry Nersesyan 22 Dec 2017 12:23 30 Jun 2018 22:56

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