Abstract
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.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 552-563 https://doi.org/10.4213/mzm12468.
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Ivochkina, N.M., Prokof’eva, S.I. & Yakunina, G.V. Integral Inequalities in the Theory of Hessian Operators. Math Notes 109, 570–579 (2021). https://doi.org/10.1134/S0001434621030251
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DOI: https://doi.org/10.1134/S0001434621030251