Isoperimetric inequalities for convex cones
HTML articles powered by AMS MathViewer
- by Pierre-Louis Lions and Filomena Pacella PDF
- Proc. Amer. Math. Soc. 109 (1990), 477-485 Request permission
Abstract:
We present here an isoperimetric inequality for sets contained in a convex cone. Some applications to symmetrization problems and Sobolev inequalities are also indicated.References
- A. Alvino, P.-L. Lions, and G. Trombetti, A remark on comparison results via symmetrization, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), no. 1-2, 37–48. MR 837159, DOI 10.1017/S0308210500014475 G. Anzellotti, M. Giaquinta, U. Massari, G. Modica, and L. Pepe, Note sul problema di Plateau, Pisa, Editrice Tecnico Scientifica, 1974.
- Catherine Bandle, Isoperimetric inequalities and applications, Monographs and Studies in Mathematics, vol. 7, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980. MR 572958
- Henri Berestycki and Filomena Pacella, Symmetry properties for positive solutions of elliptic equations with mixed boundary conditions, J. Funct. Anal. 87 (1989), no. 1, 177–211. MR 1025886, DOI 10.1016/0022-1236(89)90007-4
- Ennio De Giorgi, Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213 (Italian). MR 62214, DOI 10.1007/BF02412838
- Ennio De Giorgi, Sulla proprietà isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 5 (1958), 33–44 (Italian). MR 98331
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325 S. Gallot, Some links between isoperimetry, spectrum and topology, in preparation.
- B. Gidas, Wei Ming Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), no. 3, 209–243. MR 544879
- Enrico Giusti, The equilibrium configuration of liquid drops, J. Reine Angew. Math. 321 (1981), 53–63. MR 597979, DOI 10.1515/crll.1981.321.53
- Eduardo Gonzalez and Gabriele Greco, Una nuova dimostrazione della proprietà isoperimetrica dell’ipersfera nella classe degli insiemi aventi perimetro finito, Ann. Univ. Ferrara Sez. VII (N.S.) 23 (1977), 251–256 (1978) (Italian, with English summary). MR 467475
- E. Gonzalez, U. Massari, and I. Tamanini, On the regularity of boundaries of sets minimizing perimeter with a volume constraint, Indiana Univ. Math. J. 32 (1983), no. 1, 25–37. MR 684753, DOI 10.1512/iumj.1983.32.32003 M. Gromov, Paul Levy’s isoperimetric inequality, Prépublication I.H.E.S., 1980.
- H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0102775
- P.-L. Lions, F. Pacella, and M. Tricarico, Best constants in Sobolev inequalities for functions vanishing on some part of the boundary and related questions, Indiana Univ. Math. J. 37 (1988), no. 2, 301–324. MR 963504, DOI 10.1512/iumj.1988.37.37015 V. G. Maz’ja, Sobolev spaces, Springer-Verlag, 1985.
- Filomena Pacella and Mariarosaria Tricarico, Symmetrization for a class of elliptic equations with mixed boundary conditions, Atti Sem. Mat. Fis. Univ. Modena 34 (1985/86), no. 1, 75–93. MR 876139
- G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, No. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 477-485
- MSC: Primary 52A40; Secondary 35K20, 49F99
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000160-1
- MathSciNet review: 1000160