Abstract
We justify new integral inequalities with sharp constants for real-valued functions vanishing on the boundary of a domain of Euclidean space on assuming the domain lambda-close to convex. In particular, the closure of such domain is weakly convex in the sense of Efimov–Stechkin and Vial. We describe both standard and strengthen Hardy-type inequalities when instead of the gradients of test functions we use the inner products of the gradients of the distance function from a point to the boundary of the domain by test functions. To prove our main theorem, we apply several lemmas of significance in their own right.
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The work performed under the development program of the Volga Region Mathematical Center (Agreement 075–02–2021–1393))
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 3, pp. 481–499. https://doi.org/10.33048/smzh.2022.63.301
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Avkhadiev, F.G. Hardy-Type Inequalities with Sharp Constants in Domains Lambda-Close to Convex. Sib Math J 63, 395–411 (2022). https://doi.org/10.1134/S0037446622030016
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DOI: https://doi.org/10.1134/S0037446622030016