The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations - Hayk Ghazaryan (National Academy of Sciences of Armenia)
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(ξ) $ (of a linear differential operator $ P (D) $) in the behavior of $ P(ξ) $ 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).
Keywords: Field theory and polynomials