Natural Sciences, Mathematics, 2026
The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations
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Submitted: 2024-12-17
© 2026 by author(s) and The Gufo Inc.
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Abstract
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.