Estimates for torsional rigidity of convex domain via new geometric characteristics
DOI:
https://doi.org/10.13108/2024-16-3-21Keywords:
convex domain, function of distance to the boundary, torsional rigidity, isoperimetric inequality, extremal domainAbstract
We introduce new geometric characteristics of a convex domain with finite boundary length and provide an algorithm for calculating them. A series of isoperimetric inequalities between new functionals and known integral characteristics of the domain are proved. Some of the inequalities have a wide class of extremal domains. We consider applications of new characteristics to the problem on estimating the torsional rigidity of a convex domain.
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12.09.2024
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