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

Author(s)

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

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.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/132 Armenian Journal of Mathematics, 9(2) 102-145

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Keywords

Newton polyhedron, non-degenerate operator (equation), (almost) hypoelliptic operator (equation), multi -anisotropic Sobolev and Gevrey spaces

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