메뉴 건너뛰기




Volumn 104, Issue 1, 2000, Pages 113-127

Carleman inequalities and the heat operator

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034660768     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-00-10415-2     Document Type: Article
Times cited : (80)

References (41)
  • 3
    • 0001104071 scopus 로고
    • A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
    • N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) 36 (1957), 235-249.
    • (1957) J. Math. Pures Appl , vol.36 , Issue.9 , pp. 235-249
    • Aronszajn, N.1
  • 4
    • 0000276285 scopus 로고
    • A unique continuation theorem for exterior differential forms on Riemannian manifolds
    • N. Aronszajn, A. Krzywicki, and J. Szarski, A unique continuation theorem for exterior differential forms on Riemannian manifolds, Ark. Mat. 4 (1962), 417-453.
    • (1962) Ark. Mat , vol.4 , pp. 417-453
    • Aronszajn, N.1    Krzywicki, A.2    Szarski, J.3
  • 5
    • 84972553477 scopus 로고
    • Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms, Illinois
    • B. Barcelo, C. E. Kenig, A. Ruiz, and C. D. Sogge, Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms, Illinois J. Math. 32 (1988), 230-245.
    • (1988) J. Math , vol.32 , pp. 230-245
    • Barcelo, B.1    Kenig, C.E.2    Ruiz, A.3    Sogge, C.D.4
  • 6
    • 0004234640 scopus 로고
    • Interpolation Spaces: An Introduction, Grundlehren
    • Springer, Berlin
    • J. Bergh and J. Lõfstrõm, Interpolation Spaces: An Introduction, Grundlehren Math. Wiss. 223, Springer, Berlin, 1976.
    • (1976) Math. Wiss , vol.223
    • Bergh, J.1    Lõfstrõm, J.2
  • 7
    • 0002048855 scopus 로고
    • Surle spectreponctuel de l'opérateur de Schrodinger
    • A.-M. Berthier, Surle spectreponctuel de l'opérateur de Schrodinger, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), A393-A395.
    • (1980) C. R. Acad. Sci. Paris Sér. A-B , vol.290 , pp. A393-A395
    • Berthier, A.-M.1
  • 8
    • 0002554964 scopus 로고
    • Sur un problème d'unicitépur les systèmes d'équations aux dérivéespartielles à deux variables indépendantes
    • T. Carleman, Sur un problème d'unicitépur les systèmes d'équations aux dérivéespartielles à deux variables indépendantes, Ark. Mat., Astr. Fys. 26 (1939), no. 17.
    • (1939) Ark. Mat., Astr. Fys , vol.26 , pp. 17
    • Carleman, T.1
  • 9
    • 84966198953 scopus 로고
    • Unique continuation for A + V and the C. Fefferman-Phong class
    • S. Chanillo and E. Sawyer, Unique continuation for A + V and the C. Fefferman-Phong class, Trans. Amer. Math. Soc. 318 (1990), 275-300.
    • (1990) Trans. Amer. Math. Soc , vol.318 , pp. 275-300
    • Chanillo, S.1    Sawyer, E.2
  • 10
    • 0032328374 scopus 로고    scopus 로고
    • A strong unique continuation theorem for parabolic equations
    • X. Y. Chen, A strong unique continuation theorem for parabolic equations, Math. Ann. 311 (1998), 603-630.
    • (1998) Math. Ann , vol.311 , pp. 603-630
    • Chen, X.Y.1
  • 11
    • 0001472263 scopus 로고
    • Über die eindeutige Bestimmtheit der Losungen elliptischer Differentialglei-chungen durch Anfangsvorgaben
    • H. O. Cordes, Über die eindeutige Bestimmtheit der Losungen elliptischer Differentialglei-chungen durch Anfangsvorgaben, Nachr. Akad. Wiss. Gottingen. Math-Phys. Kl. IIa 1956, 239-258.
    • (1956) Nachr. Akad. Wiss. Gottingen. Math-Phys. Kl. Iia , pp. 239-258
    • Cordes, H.O.1
  • 12
    • 0001030873 scopus 로고
    • A partial answer to a conjecture of B. Simon concerning unique continuation
    • E. B. Fabes, N. Garofalo, and F. H. Lin, A partial answer to a conjecture of B. Simon concerning unique continuation, J. Funct. Anal. 88 (1990), 194-210.
    • (1990) J. Funct. Anal , vol.88 , pp. 194-210
    • Fabes, E.B.1    Garofalo, N.2    Lin, F.H.3
  • 13
    • 0001109545 scopus 로고
    • Monotonicity properties of variational integrals, Ap-weights and unique continuation
    • p-weights and unique continuation, Indiana Univ. Math. J. 35 (1986), 245-268.
    • (1986) Indiana Univ. Math. J , vol.35 , pp. 245-268
    • Garofalo, N.1    Lin, F.H.2
  • 14
    • 84990604274 scopus 로고
    • Unique continuation for elliptic operators: A geometric-variational approach
    • N. Garofalo and F. H. Lin, Unique continuation for elliptic operators: A geometric-variational approach, Comm. Pure Appl. Math. 40 (1987), 347-366.
    • (1987) Comm. Pure Appl. Math , vol.40 , pp. 347-366
    • Garofalo, N.1    Lin, F.H.2
  • 15
    • 0002034548 scopus 로고
    • On the unique continuation property for Schrodinger Hamiltonians
    • V. Georgescu, On the unique continuation property for Schrodinger Hamiltonians, Helv. Phys. Acta 52 (1979), 655-670.
    • (1979) Helv. Phys. Acta , vol.52 , pp. 655-670
    • Georgescu, V.1
  • 16
    • 0002188503 scopus 로고
    • Uniqueness theorems for second order elliptic differential equations
    • L. Hormander, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), 21-64.
    • (1983) Comm. Partial Differential Equations , vol.8 , pp. 21-64
    • Hormander, L.1
  • 17
    • 0043024363 scopus 로고
    • A unique continuation theorem for solutions of a parabolic differential equation
    • S. Ito and H. Yamabe, A unique continuation theorem for solutions of a parabolic differential equation, J. Math. Soc. Japan 10 (1958), 314-321.
    • (1958) J. Math. Soc. Japan , vol.10 , pp. 314-321
    • Ito, S.1    Yamabe, H.2
  • 18
    • 0038953298 scopus 로고
    • Carleman inequalities for the Dirac and Laplace operators and unique continuation
    • D. Jerison, Carleman inequalities for the Dirac and Laplace operators and unique continuation, Adv. Math. 62 (1986), 118-134.
    • (1986) Adv. Math , vol.62 , pp. 118-134
    • Jerison, D.1
  • 19
    • 0001226256 scopus 로고
    • Unique continuation and absence of positive eigenvalues for Schrodinger operators
    • D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrodinger operators, Ann. of Math. (2) 121 (1985), 463-494.
    • (1985) Ann. of Math , vol.121 , Issue.2 , pp. 463-494
    • Jerison, D.1    Kenig, C.E.2
  • 20
    • 0003364279 scopus 로고
    • Partial Differential Equations
    • 4th ed, Springer, New York
    • F. John, Partial Differential Equations, 4th ed., Appl. Math. Sci. 1, Springer, New York, 1982.
    • (1982) Appl. Math. Sci , vol.1
    • John, F.1
  • 21
  • 22
    • 84990569674 scopus 로고
    • Unique continuation in geometry
    • J. L. Kazdan, Unique continuation in geometry, Comm. Pure Appl. Math. 41 (1988), 667-681.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 667-681
    • Kazdan, J.L.1
  • 23
    • 84972558685 scopus 로고
    • Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
    • C. E. Kenig, A. Ruiz, and C. D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), 329-347.
    • (1987) Duke Math. J , vol.55 , pp. 329-347
    • Kenig, C.E.1    Ruiz, A.2    Sogge, C.D.3
  • 24
    • 0001242177 scopus 로고
    • A unique continuation theorem for uniformly elliptic equations with strongly singular potentials
    • K. Kurata, A unique continuation theorem for uniformly elliptic equations with strongly singular potentials, Comm. Partial Differential Equations 18 (1993), 1161-1189.
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 1161-1189
    • Kurata, K.1
  • 25
    • 84990553493 scopus 로고
    • A uniqueness theorem for parabolic equations
    • F.-H. Lin, A uniqueness theorem for parabolic equations, Comm. Pure Appl. Math. 43 (1990), 127-136.
    • (1990) Comm. Pure Appl. Math , vol.43 , pp. 127-136
    • Lin, F.-H.1
  • 26
    • 84990619714 scopus 로고
    • Nodal sets of solutions of elliptic and parabolic equations
    • F.-H. Lin, Nodal sets of solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 44 (1991), 287-308.
    • (1991) Comm. Pure Appl. Math , vol.44 , pp. 287-308
    • Lin, F.-H.1
  • 27
    • 0001446993 scopus 로고    scopus 로고
    • Unique continuation for parabolic equations
    • C.-C. Poon, Unique continuation for parabolic equations, Comm. Partial Differential Equations 21 (1996), 521-539.
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 521-539
    • Poon, C.-C.1
  • 28
    • 0003136982 scopus 로고
    • Calderón-Zygmund theory for operatorvalued kernels
    • J. L. Rubio de Francia, F. J. Ruiz, and J. L. Torrea, Calderón-Zygmund theory for operatorvalued kernels, Adv. Math. 62 (1988), 7-48.
    • (1988) Adv. Math , vol.62 , pp. 7-48
    • Rubio De Francia, J.L.1    Ruiz, F.J.2    Torrea, J.L.3
  • 29
    • 0000523343 scopus 로고
    • Unique continuation for some evolution equations
    • J.-C. Saut and B. Scheurer, Unique continuation for some evolution equations, J. Differential Equations 66 (1987), 118-139.
    • (1987) J. Differential Equations , vol.66 , pp. 118-139
    • Saut, J.-C.1    Scheurer, B.2
  • 30
    • 0002064069 scopus 로고
    • Unique continuation for Schrodinger operators in dimensions three or less
    • E. T. Sawyer, Unique continuation for Schrodinger operators in dimensions three or less, Ann. Inst. Fourier (Grenoble) 34 (1984), 189-200.
    • (1984) Ann. Inst. Fourier (Grenoble) , vol.34 , pp. 189-200
    • Sawyer, E.T.1
  • 31
    • 84988167463 scopus 로고
    • Unique continuation for Schrodinger operators with unbounded potentials
    • M. Schechter and B. Simon, Unique continuation for Schrodinger operators with unbounded potentials, J. Math. Anal. Appl. 77 (1980), 482-492.
    • (1980) J. Math. Anal. Appl , vol.77 , pp. 482-492
    • Schechter, M.1    Simon, B.2
  • 32
    • 84968468449 scopus 로고
    • Oscillatory integrals and unique continuation for second order elliptic differential equations
    • C. D. Sogge, Oscillatory integrals and unique continuation for second order elliptic differential equations, J. Amer. Math. Soc. 2 (1989), 491-515.
    • (1989) J. Amer. Math. Soc , vol.2 , pp. 491-515
    • Sogge, C.D.1
  • 33
    • 0002225325 scopus 로고
    • Strong uniqueness theorems for second order elliptic differential equations
    • C. D. Sogge, Strong uniqueness theorems for second order elliptic differential equations, Amer. J. Math. 112 (1990), 943-984.
    • (1990) Amer. J. Math , vol.112 , pp. 943-984
    • Sogge, C.D.1
  • 34
    • 0002064071 scopus 로고
    • A unique continuation theorem for second order parabolic differential operators
    • C. D. Sogge, A unique continuation theorem for second order parabolic differential operators, Ark. Mat. 28 (1990), 159-182.
    • (1990) Ark. Mat , vol.28 , pp. 159-182
    • Sogge, C.D.1
  • 35
    • 0001174972 scopus 로고
    • Interpolation of linear operators
    • E. M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492.
    • (1956) Trans. Amer. Math. Soc , vol.83 , pp. 482-492
    • Stein, E.M.1
  • 36
    • 0003201639 scopus 로고
    • Singular Integrals and Differentiability Properties of Functions
    • Princeton Univ. Press, Princeton
    • E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser. 30, Princeton Univ. Press, Princeton, 1970.
    • (1970) Princeton Math. Ser , vol.30
    • Stein, E.M.1
  • 37
    • 0003244651 scopus 로고
    • Lectures on Hermite and Laguerre Expansions
    • Princeton Univ. Press, Princeton
    • S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Math. Notes 42, Princeton Univ. Press, Princeton, 1993.
    • (1993) Math. Notes , vol.42
    • Thangavelu, S.1
  • 38
    • 0002064073 scopus 로고    scopus 로고
    • Hermite and special Hermite expansions revisited
    • S. Thangavelu, Hermite and special Hermite expansions revisited, Duke Math. J. 94 (1998), 257-278.
    • (1998) Duke Math. J , vol.94 , pp. 257-278
    • Thangavelu, S.1
  • 39
    • 0000800471 scopus 로고
    • Unique continuation for Δu ≤ V Δu and related problems
    • T. Wolff, Unique continuation for Δu ≤ V Δu and related problems, Rev. Mat. Iberoamer-icana 6 (1990), 155-200.
    • (1990) Rev. Mat. Iberoamer-Icana , vol.6 , pp. 155-200
    • Wolff, T.1
  • 40
    • 0000339742 scopus 로고
    • A property of measures in R" and an application to unique continuation
    • T. Wolff, A property of measures in R" and an application to unique continuation, Geom. Funct. Anal. 2 (1992), 225-284.
    • (1992) Geom. Funct. Anal , vol.2 , pp. 225-284
    • Wolff, T.1
  • 41
    • 0001139058 scopus 로고
    • A unique continuation theorem of a diffusion equation
    • H. Yamabe, A unique continuation theorem of a diffusion equation, Ann. of Math. (2) 69 (1959), 462-466.
    • (1959) Ann. of Math , vol.69 , Issue.2 , pp. 462-466
    • Yamabe, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.