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

Armenian Journal of Mathematics

Haik Ghazaryan¹ 

[1] Russian - Armenian (Slavonic) University, Institute of Mathematicsof National Academy of Armenia, Yerevan;

关键词: Newton polyhedron;    non-degenerate operator (equation);    (almost) hypoelliptic operator (equation);    multi -anisotropic Sobolev and Gevrey spaces;   

DOI  :  

来源: DOAJ

【 摘 要 】

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(\xi) $  ( of a linear differential operator  $ P ( D) $) in the behaviour of  $ P(\xi) $ at infinity and in the smoothness of solutions of the equation $  P ( D)u = f. $

【 授权许可】

Unknown