Integral Inequalities in the Theory of Hessian Operators

N. M. Ivochkina ; S. I. Prokof'eva ; G. V. Yakunina

Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 552-563.

Résumé

The paper discusses the influence of new geometric invariants of domains on Hessian integral inequalities and provides a new proof of the well-known Trudinger–Wang inequalities. A comparative analysis of the Trudinger–Wang inequalities with the classical Poincaré–Friedrichs inequality is carried out; it shows that these inequalities are qualitatively different. It is shown that Hessian integral inequalities contain information of new type and have no analogues in classical functional analysis.

Détail

Keywords: Hessian operators, Hessian integrals, Gårding cones
Mots-clés : $p$-convex hypersurfaces.

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