Geodesic
Estimates for torsional rigidity of convex domain via new geometric characteristics
Ufa mathematical journal, Tome 16 (2024) no. 3, pp. 21-39

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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.
Keywords: function of distance to the boundary, torsional rigidity, isoperimetric inequality, extremal domain.
Mots-clés : convex domain 
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     author = {L. I. Gafiyatullina and R. G. Salakhudinov},
     title = {Estimates for torsional rigidity of  convex domain via new geometric characteristics},
     journal = {Ufa mathematical journal},
     pages = {21--39},
     publisher = {mathdoc},
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     number = {3},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2024_16_3_a1/}
}
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L. I. Gafiyatullina; R. G. Salakhudinov. Estimates for torsional rigidity of  convex domain via new geometric characteristics. Ufa mathematical journal, Tome 16 (2024) no. 3, pp. 21-39. http://geodesic.mathdoc.fr/item/UFA_2024_16_3_a1/