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

Haik Ghazaryan

Received N/A; revised N/A; accepted N/A

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

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.

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

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