Coercive estimates for multilayer degenerate differential operators

H. G. Kazaryan

Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 99-120.

Résumé

We obtain the conditions under which a given multilayer differential operator $P(D)$ (polynomial $P(\xi)$) is more powerful than operator $Q(D)$ (polynomial $Q(\xi)$). This is used to obtain estimates of monomials, which, in turn, using the theory of Fourier multipliers, is used to obtain coercive estimates of derivatives of functions through the differential operator $P(D)$ applied to these functions.

Détail

Keywords: coercive estimate, comparison of power of differential operators (polynomials), lower-order term of differential operator (polynomial), Newton polyhedron, degenerate (nondegenerate) operator (polynomial), multilayer operator (polynomial).

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