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Volumn 50, Issue 1, 2007, Pages 35-47

A singular critical potential for the schrödinger operator

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EID: 33947363826     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-2007-004-3     Document Type: Article
Times cited : (18)

References (16)
  • 1
    • 3142721916 scopus 로고    scopus 로고
    • Dispersion and Strichartz inequalities for Schrödinger equations with singular coefficients
    • V. Banica, Dispersion and Strichartz inequalities for Schrödinger equations with singular coefficients. SIAM J. Math. Anal. 35(2003), no. 4, 868-883.
    • (2003) SIAM J. Math. Anal , vol.35 , Issue.4 , pp. 868-883
    • Banica, V.1
  • 2
    • 0036361205 scopus 로고    scopus 로고
    • Semi-classical estimates for the resolvent in nontrapping geometries
    • N. Burq, Semi-classical estimates for the resolvent in nontrapping geometries. Internat. Math. Res. Notices (2002), no. 5, 221-241.
    • (2002) Internat. Math. Res. Notices , Issue.5 , pp. 221-241
    • Burq, N.1
  • 3
    • 3142714420 scopus 로고    scopus 로고
    • Smoothing effect for Schrödinger boundary value problems
    • N. Burq, Smoothing effect for Schrödinger boundary value problems. Duke Math. J. 123(2004), no. 2, 403-427.
    • (2004) Duke Math. J , vol.123 , Issue.2 , pp. 403-427
    • Burq, N.1
  • 5
    • 0141503424 scopus 로고    scopus 로고
    • N. Burq, F. Planchon, J. G. Stalker, and A. Shadi Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential. J. Funct. Anal. 203(2003), no. 2, 519-549.
    • N. Burq, F. Planchon, J. G. Stalker, and A. Shadi Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential. J. Funct. Anal. 203(2003), no. 2, 519-549.
  • 6
    • 0036025289 scopus 로고    scopus 로고
    • Concentration and lack of observability of waves in highly heterogeneous media
    • C. Castro and E. Zuazua, Concentration and lack of observability of waves in highly heterogeneous media. Arch. Rational Mech. Anal. 164(2002), no. 1, 39-72.
    • (2002) Arch. Rational Mech. Anal , vol.164 , Issue.1 , pp. 39-72
    • Castro, C.1    Zuazua, E.2
  • 7
    • 0000497589 scopus 로고
    • Local smoothing properties of Schrödinger equations
    • P. Constantin and J. C. Saut, Local smoothing properties of Schrödinger equations. Indiana Univ. Math. J. 38(1989), no. 3, 791-810.
    • (1989) Indiana Univ. Math. J , vol.38 , Issue.3 , pp. 791-810
    • Constantin, P.1    Saut, J.C.2
  • 8
    • 24344446431 scopus 로고    scopus 로고
    • On the wave equation with a large rough potential
    • P. D'Ancona and V. Pierfelice, On the wave equation with a large rough potential. J. Funct. Anal. 227(2005), no. 1, 30-77.
    • (2005) J. Funct. Anal , vol.227 , Issue.1 , pp. 30-77
    • D'Ancona, P.1    Pierfelice, V.2
  • 9
    • 33947369876 scopus 로고    scopus 로고
    • Inégalités de résolvante pour l'opérateur de Schrödinger avec potentiel multipolaire critique
    • T. Duyckaerts, Inégalités de résolvante pour l'opérateur de Schrödinger avec potentiel multipolaire critique. Bull. Soc. Math. France 134(2006), no. 2, 201-239.
    • (2006) Bull. Soc. Math. France , vol.134 , Issue.2 , pp. 201-239
    • Duyckaerts, T.1
  • 11
    • 0003352781 scopus 로고
    • Methods of Modern Mathematical Physics. II
    • Academic Press, San Diego
    • M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier analysis, self-adjointness. Academic Press, San Diego, 1975.
    • (1975) Fourier analysis, self-adjointness
    • Reed, M.1    Simon, B.2
  • 12
    • 1542508715 scopus 로고    scopus 로고
    • Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
    • I. Rodnianski and W. Schlag. Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Invent. Math. 155(2004), no. 3, 451-513.
    • (2004) Invent. Math , vol.155 , Issue.3 , pp. 451-513
    • Rodnianski, I.1    Schlag, W.2
  • 13
    • 84974001039 scopus 로고
    • Local regularity of solutions to wave with time-dependent potentials
    • A. Ruiz and L. Vega, Local regularity of solutions to wave with time-dependent potentials. Duke Math. J. 76(1994), no. 3, 913-940.
    • (1994) Duke Math. J , vol.76 , Issue.3 , pp. 913-940
    • Ruiz, A.1    Vega, L.2
  • 14
    • 0001679726 scopus 로고
    • Regularity of solutions to the Schrödinger equation
    • P. Sjölin, Regularity of solutions to the Schrödinger equation. Duke Math. J. 55(1987), no. 3, 699-715.
    • (1987) Duke Math. J , vol.55 , Issue.3 , pp. 699-715
    • Sjölin, P.1
  • 15
    • 0001427886 scopus 로고    scopus 로고
    • Global Strichartz estimates for non-trapping perturbations of the Laplacian
    • H. F. Smith and C. D. Sogge, Global Strichartz estimates for non-trapping perturbations of the Laplacian. Comm. Partial Differential Equations 25(2000), no. 11-12, 2171-2183.
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.11-12 , pp. 2171-2183
    • Smith, H.F.1    Sogge, C.D.2
  • 16
    • 0000801121 scopus 로고
    • Schrödinger equations: Pointwise convergence to the initial data
    • L. Vega, Schrödinger equations: pointwise convergence to the initial data. Proc. Amer. Math. Soc. 102(1988), no. 4, 874-878.
    • (1988) Proc. Amer. Math. Soc , vol.102 , Issue.4 , pp. 874-878
    • Vega, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.