The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations - Ghazaryan, Haik (Armenian Journal of Mathematics, 2017)
In the paper we investigate the role of the Newton polyhedron , which generates a multianisotropic Sobolev space W_p^ and Gevrey space G^, and the role of the Newton polyhedron ( P) of a polynomial P(ξ) ( of a linear differential operator P ( D) ) in the behaviour of P(ξ) at infinity and in the smoothness of solutions of the equation P ( D)u = f.