메뉴 건너뛰기




Volumn 23, Issue 4, 2006, Pages 539-565

Anisotropic symmetrization

Author keywords

Convex symmetrization; Hardy inequality; Isoperimetric inequality; P lya Szego combining double acute accent inequality; Riesz Sobolev rearrangement inequality; Sobolev inequality; Steiner symmetrization; Symmetric rearrangement; Wulff's crystal

Indexed keywords

NUMERICAL METHODS; PROBLEM SOLVING;

EID: 33745684978     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2005.06.001     Document Type: Article
Times cited : (58)

References (31)
  • 1
    • 0003362526 scopus 로고
    • Sobolev Spaces
    • Academic Press, New York
    • Adams R.A. Sobolev Spaces. Pure Appl. Math. vol. 65 (1975), Academic Press, New York
    • (1975) Pure Appl. Math. , vol.65
    • Adams, R.A.1
  • 3
    • 0001002414 scopus 로고
    • On optimization problems with prescribed rearrangements
    • Alvino A., Trombetti G., and Lions P.-L. On optimization problems with prescribed rearrangements. Nonlinear Anal. 13 2 (1989) 185-220
    • (1989) Nonlinear Anal. , vol.13 , Issue.2 , pp. 185-220
    • Alvino, A.1    Trombetti, G.2    Lions, P.-L.3
  • 4
    • 0002572462 scopus 로고
    • A unified approach to symmetrization
    • Partial Equations of Elliptic Type. Alvino A., et al. (Ed), Cambridge University Press, Cambridge
    • Baernstein II A. A unified approach to symmetrization. In: Alvino A., et al. (Ed). Partial Equations of Elliptic Type. Sympos. Math. vol. 35 (1995), Cambridge University Press, Cambridge 47-49
    • (1995) Sympos. Math. , vol.35 , pp. 47-49
    • Baernstein II, A.1
  • 5
    • 0001378271 scopus 로고
    • A general rearrangement inequality for multiple integrals
    • Brascamp H.J., Lieb E.H., and Luttinger J.M. A general rearrangement inequality for multiple integrals. J. Funct. Anal. 17 (1974) 227-237
    • (1974) J. Funct. Anal. , vol.17 , pp. 227-237
    • Brascamp, H.J.1    Lieb, E.H.2    Luttinger, J.M.3
  • 6
    • 23044519317 scopus 로고    scopus 로고
    • An approach to symmetrization via polarization
    • Brock F., and Solynin A.Yu. An approach to symmetrization via polarization. Trans. Amer. Math. Soc. 352 4 (2000) 1759-1796
    • (2000) Trans. Amer. Math. Soc. , vol.352 , Issue.4 , pp. 1759-1796
    • Brock, F.1    Solynin, A.Yu.2
  • 7
    • 0030535181 scopus 로고    scopus 로고
    • Cases of equality in the Riesz rearrangement inequality
    • Burchard A. Cases of equality in the Riesz rearrangement inequality. Ann. of Math. (2) 143 3 (1996) 499-527
    • (1996) Ann. of Math. (2) , vol.143 , Issue.3 , pp. 499-527
    • Burchard, A.1
  • 9
    • 0000464558 scopus 로고
    • The isoperimetric problem for Minkowski area
    • Busemann H. The isoperimetric problem for Minkowski area. Amer. J. Math. 71 (1949) 743-762
    • (1949) Amer. J. Math. , vol.71 , pp. 743-762
    • Busemann, H.1
  • 12
    • 0039481273 scopus 로고
    • Wulff theorem and best constant in Sobolev inequality
    • Dacorogna B., and Pfister C.-E. Wulff theorem and best constant in Sobolev inequality. J. Math. Pures Appl. (9) 71 2 (1992) 97-118
    • (1992) J. Math. Pures Appl. (9) , vol.71 , Issue.2 , pp. 97-118
    • Dacorogna, B.1    Pfister, C.-E.2
  • 13
    • 0003244186 scopus 로고
    • Convex Analysis and Variational Problems
    • North-Holland Publishing Co., Amsterdam
    • Ekeland I., and Temam R. Convex Analysis and Variational Problems. Stud. Math. Appl. vol. 1 (1976), North-Holland Publishing Co., Amsterdam
    • (1976) Stud. Math. Appl. , vol.1
    • Ekeland, I.1    Temam, R.2
  • 15
  • 16
    • 33745731549 scopus 로고
    • On the shape of solutions to some variational problems
    • Prague, 1994, Prometheus, Prague
    • Kawohl B. On the shape of solutions to some variational problems. Nonlinear Analysis, Function Spaces and Applications, vol. 5. Prague, 1994 (1994), Prometheus, Prague 77-102
    • (1994) Nonlinear Analysis, Function Spaces and Applications, vol. 5 , pp. 77-102
    • Kawohl, B.1
  • 17
    • 0003269816 scopus 로고
    • Rearrangements and Convexity of Level Sets in PDE
    • Springer-Verlag, Berlin
    • Kawohl B. Rearrangements and Convexity of Level Sets in PDE. Lecture Notes in Math. vol. 1150 (1985), Springer-Verlag, Berlin
    • (1985) Lecture Notes in Math. , vol.1150
    • Kawohl, B.1
  • 18
    • 33745689275 scopus 로고    scopus 로고
    • On the symmetrization of anisotropic integral functionals
    • Klimov V.S. On the symmetrization of anisotropic integral functionals. Izv. Vyssh. Uchebn. Zaved. Mat. 8 (1999) 26-32
    • (1999) Izv. Vyssh. Uchebn. Zaved. Mat. , Issue.8 , pp. 26-32
    • Klimov, V.S.1
  • 19
    • 0242648945 scopus 로고    scopus 로고
    • Analysis
    • American Mathematical Society, Providence, RI
    • Lieb E.H., and Loss M. Analysis. Grad. Stud. Math. second ed. vol. 14 (2001), American Mathematical Society, Providence, RI
    • (2001) Grad. Stud. Math. second ed. , vol.14
    • Lieb, E.H.1    Loss, M.2
  • 20
    • 0000296501 scopus 로고
    • Symétrie et compacité dans les espaces de Sobolev
    • Lions P.-L. Symétrie et compacité dans les espaces de Sobolev. J. Funct. Anal. 49 3 (1982) 315-334
    • (1982) J. Funct. Anal. , vol.49 , Issue.3 , pp. 315-334
    • Lions, P.-L.1
  • 21
    • 0004027912 scopus 로고
    • Inégalités isopérimétriques et applications en physique
    • Hermann, Paris
    • Mossino J. Inégalités isopérimétriques et applications en physique. Travaux en cours (1984), Hermann, Paris
    • (1984) Travaux en cours
    • Mossino, J.1
  • 23
    • 0037932537 scopus 로고
    • Symmetrization of condensers in n-space
    • Sarvas J. Symmetrization of condensers in n-space. Ann. Acad. Sci. Fenn., Ser. A I 522 (1972) 1-44
    • (1972) Ann. Acad. Sci. Fenn., Ser. A I , vol.522 , pp. 1-44
    • Sarvas, J.1
  • 24
    • 0004184184 scopus 로고
    • Probability for Analysts
    • Chapman & Hall, New York Lecture notes prepared by Kuppusamy Ravindran
    • Stromberg K.R. Probability for Analysts. Chapman & Hall Probability Series (1994), Chapman & Hall, New York Lecture notes prepared by Kuppusamy Ravindran
    • (1994) Chapman & Hall Probability Series
    • Stromberg, K.R.1
  • 25
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • Talenti G. Best constant in Sobolev inequality. Ann. Mat. Pura Appl. (4) 110 (1976) 353-372
    • (1976) Ann. Mat. Pura Appl. (4) , vol.110 , pp. 353-372
    • Talenti, G.1
  • 26
    • 0039007378 scopus 로고
    • On isoperimetric theorems of mathematical physics
    • Gruber P.M., and Wills J. (Eds), Elsevier Science, Amsterdam
    • Talenti G. On isoperimetric theorems of mathematical physics. In: Gruber P.M., and Wills J. (Eds). Handbook of Convex Geometry B (1993), Elsevier Science, Amsterdam 1131-1147
    • (1993) Handbook of Convex Geometry B , pp. 1131-1147
    • Talenti, G.1
  • 27
    • 84966261517 scopus 로고
    • Crystalline variational problems
    • Taylor J.E. Crystalline variational problems. Bull. Amer. Math. Soc. 84 4 (1978) 568-588
    • (1978) Bull. Amer. Math. Soc. , vol.84 , Issue.4 , pp. 568-588
    • Taylor, J.E.1
  • 28
    • 31144443743 scopus 로고    scopus 로고
    • Universal approximation of symmetrizations by polarizations
    • Van Schaftingen J. Universal approximation of symmetrizations by polarizations. Proc. Amer. Math. Soc. 134 1 (2006) 177-186
    • (2006) Proc. Amer. Math. Soc. , vol.134 , Issue.1 , pp. 177-186
    • Van Schaftingen, J.1
  • 29
    • 16344365946 scopus 로고    scopus 로고
    • Set transformations, symmetrizations and isoperimetric inequalities
    • Benci V., and Masiello A. (Eds), Springer
    • Van Schaftingen J., and Willem M. Set transformations, symmetrizations and isoperimetric inequalities. In: Benci V., and Masiello A. (Eds). Nonlinear Analysis and Applications to the Physical Sciences (2004), Springer 135-152
    • (2004) Nonlinear Analysis and Applications to the Physical Sciences , pp. 135-152
    • Van Schaftingen, J.1    Willem, M.2
  • 31
    • 0003320023 scopus 로고
    • Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation
    • Springer-Verlag, New York
    • Ziemer W.P. Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation. Grad. Texts in Math. vol. 120 (1989), Springer-Verlag, New York
    • (1989) Grad. Texts in Math. , vol.120
    • Ziemer, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.