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 $ \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 behaviour of $ P(ξ) $ at infinity and in the smoothness of solutions of the equation $ P ( D)u = f. $
Keywords: Newton polyhedron; non-degenerate operator (equation); (almost) hypoelliptic operator (equation); multi -anisotropic Sobolev and Gevrey spaces