Geodesic
Integral Inequalities in the Theory of Hessian Operators
Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 552-563

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Hessian operators, Hessian integrals, Gårding cones
Mots-clés : $p$-convex hypersurfaces. 
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     author = {N. M. Ivochkina and S. I. Prokof'eva and G. V. Yakunina},
     title = {Integral {Inequalities} in the {Theory} of {Hessian} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {552--563},
     publisher = {mathdoc},
     volume = {109},
     number = {4},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a5/}
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N. M. Ivochkina; S. I. Prokof'eva; G. V. Yakunina. Integral Inequalities in the Theory of Hessian Operators. Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 552-563. http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a5/