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Volumn 107, Issue 46, 2010, Pages 19696-19701

Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

Author keywords

Gagliardo Nirenberg Sobolev; Gradient flow

Indexed keywords

ALGORITHM; ANALYTIC METHOD; CONFERENCE PAPER; DIFFUSION; FLOW KINETICS; MATHEMATICAL MODEL; PRIORITY JOURNAL;

EID: 78650528836     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1008323107     Document Type: Article
Times cited : (55)

References (16)
  • 1
    • 0000298073 scopus 로고
    • Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
    • Lieb EH (1983) Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann Math 118:349-374.
    • (1983) Ann Math , vol.118 , pp. 349-374
    • Lieb, E.H.1
  • 2
    • 0036710614 scopus 로고    scopus 로고
    • Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
    • Del Pino M, Dolbeault J (2002) Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. Journal de mathematiques pure et applique 81:301-342.
    • (2002) Journal de Mathematiques Pure et Applique , vol.81 , pp. 301-342
    • Del Pino, M.1    Dolbeault, J.2
  • 5
    • 33748896800 scopus 로고    scopus 로고
    • Global positivity estimates and Harnack inequalities for the fast diffusion equation
    • Bonforte M, Vázquez JL (2006) Global positivity estimates and Harnack inequalities for the fast diffusion equation. J Func Anal 240:399-428.
    • (2006) J Func Anal , vol.240 , pp. 399-428
    • Bonforte, M.1    Vázquez, J.L.2
  • 6
    • 0037847744 scopus 로고    scopus 로고
    • Asymptotic behavior for the porous medium equation posed in the whole space
    • Vázquez JL (2003) Asymptotic behavior for the porous medium equation posed in the whole space. J Evol Equ 3:67-118.
    • (2003) J Evol Equ , vol.3 , pp. 67-118
    • Vázquez, J.L.1
  • 7
    • 0037704920 scopus 로고    scopus 로고
    • Fine asymptotics for fast diffusion equations
    • Carrillo JA, Vázquez JL (2003) Fine asymptotics for fast diffusion equations. Comm Part Diff Eq 28:1023-1056.
    • (2003) Comm Part Diff Eq , vol.28 , pp. 1023-1056
    • Carrillo, J.A.1    Vázquez, J.L.2
  • 9
    • 78650557183 scopus 로고    scopus 로고
    • Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality, to appear in Calculus of Variations and PDEs
    • in press
    • Frank R, Lieb EH (2010) Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality, to appear in Calculus of Variations and PDEs. Calculus of Variations, in press.
    • (2010) Calculus of Variations
    • Frank, R.1    Lieb, E.H.2
  • 10
    • 84916181784 scopus 로고
    • Existence and uniqueness of the minimization solution of Choquard's nonlinear equation
    • Lieb EH (1977) Existence and uniqueness of the minimization solution of Choquard's nonlinear equation. Stud Appl Math 57:93-105.
    • (1977) Stud Appl Math , vol.57 , pp. 93-105
    • Lieb, E.H.1
  • 11
    • 0003277699 scopus 로고    scopus 로고
    • 1 decay of the porous medium equation to self-similarity
    • 1 decay of the porous medium equation to self-similarity. Indiana U Math J 46:113-142.
    • (2000) Indiana U Math J , vol.46 , pp. 113-142
    • Carrillo, J.A.1    Toscani, G.2
  • 12
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
    • Beckner W (1993) Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality. Ann Math 138:213-242.
    • (1993) Ann Math , vol.138 , pp. 213-242
    • Beckner, W.1
  • 13
    • 0002707928 scopus 로고
    • Competing symmetries, the logarithmic HLS inequality and Onofri's inequality onSn
    • Carlen EA, Loss M (1992) Competing symmetries, the logarithmic HLS inequality and Onofri's inequality onSn. Geom Funct Anal 2:90-104.
    • (1992) Geom Funct Anal , vol.2 , pp. 90-104
    • Carlen, E.A.1    Loss, M.2
  • 14
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • Otto F (2001) The geometry of dissipative evolution equations: the porous medium equation. Comm Part Diff Eq 26:101-174.
    • (2001) Comm Part Diff Eq , vol.26 , pp. 101-174
    • Otto, F.1
  • 15
    • 74949092030 scopus 로고    scopus 로고
    • A family of nonlinear fourth order equations of gradient flow type
    • Matthes D, McCann RJ, Savaré G (2009) A family of nonlinear fourth order equations of gradient flow type. Comm Part Diff Eq 34:1352-1397.
    • (2009) Comm Part Diff Eq , vol.34 , pp. 1352-1397
    • Matthes, D.1    McCann, R.J.2    Savaré, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.