RUS  ENG
Full version
JOURNALS // Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki

Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2006, Volume 148, Book 2, Pages 151–162 (Mi uzku554)

Isoperimetric inequalities for $l^p$-norms of the distance function to the boundary
R. G. Salahudinov

References

1. Avkhadiev F. G., “Solution of generalizated St Venant problem”, Sborn. Math., 189:12 (1998), 1739–1748  mathnet  crossref  mathscinet  zmath  adsnasa
2. Avkhadiev F. G., “Geometric characteristics of domains equivalent to the norms of some embedding operators”, in Russian, Proc. of the Intern. Conf. and Chebyshev Lectures, 1, Moscow State University, M., 1996, 12–14
3. Kohler-Jobin M.-Th., “Symmetrization with equal Dirichlet integrals”, SIAM J. Math. Anal., 13 (1982), 153–161  crossref  mathscinet  zmath  isi
4. Salahudinov R. G., “Isoperimetric inequality for torsional rigidity in the complex plane”, J. of Inequal. and Appl., 6 (2001), 253–260  mathscinet  zmath
5. Bañuelos R., van den Berg M., Carroll T., “Torsional Rigidity and Expected Lifetime of Brownian motion”, J. London Math. Soc., 66:2 (2002), 499–512  crossref  mathscinet  zmath
6. Davies E. B., “A review of Hardy Inequalities”, Operator Theory: Adv. Appl., 110 (1989), 55-67  mathscinet
7. Bandle C., Isoperimetric inequalities and applications, Pitman Advanced Publishing Program, Boston, 1980, 228 pp.  mathscinet  zmath
8. Kohler-Jobin M.-Th., “Une propriété de monotonie isopérimétrique qui contient plusieurs théorémes classiques”, C.R. Acad. Sci. Paris, 284:3 (1977), 917–920  mathscinet  zmath
9. Bandle C., “Bounds of the solutions of boundary value problems”, J. of Math. Anal. and Appl., 54 (1976), 706–716  crossref  mathscinet  zmath
10. Kohler-Jobin M.-Th., “Isoperimetric monotonicity and isoperimetric inequalities of Payne–Rayner type for the first eigenfunction of the Helmholtz problem”, Z. Angew. Math. Phys., 32 (1981), 625–646  crossref  mathscinet  zmath  isi
11. Hayman W. K., “Some bounds for the principal frequency”, Appl. Anal., 7 (1978), 247–254  crossref  mathscinet  zmath
12. Hersch J., “Isoperimetric monotonicity – some properties and conjectures (connection between Isoperimetric Inequalities)”, SIAM REV., 30:4 (1988), 551–577  crossref  mathscinet  zmath  isi
13. Bandle C., “Estimates for the Green's functions of Elliptic Operators”, SIAM J. Math. Anal., 9 (1978), 1126–1136  crossref  mathscinet  zmath
14. Avkhadiev F. G., Salahudinov R. G., “Isoperimetric inequalities for conformal moments of plane domains”, J. of Inequal. and Appl., 7:4 (2002), 593–601  mathscinet  zmath  isi
15. Leavitt J., Ungar P., “Circle supports the largest sandpile”, Comment. Pure Appl. Math., 15 (1962), 35–37  crossref  mathscinet  zmath
16. Avkhadiev F. G., Salahudinov R. G., “Bilateral Isoperimetric inequalities for boundary moments of plane domains”, Lobachevskii J. of Mathematics, 9 (2001), 3–5  mathnet  mathscinet  zmath; URL: http://www.ljm.ksu.ru  mathscinet
17. Schmidt E., “Über das isoperimetrische Problem im Raum von $n$ Dimensionen”, Math. Z., 44 (1938), 689–788  crossref  mathscinet


© Steklov Math. Inst. of RAS, 2026