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

  • Haik Ghazaryan Russian - Armenian (Slavonic) University, Institute of Mathematics of National Academy of Armenia, Yerevan
Keywords: Newton polyhedron, non-degenerate operator (equation), (almost) hypoelliptic operator (equation), multi -anisotropic Sobolev and Gevrey spaces

Abstract

 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. $

Published
2017-12-26
How to Cite
Ghazaryan, H. (2017). The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations. Armenian Journal of Mathematics, 9(2), 102-145. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/132
Section
Articles