메뉴 건너뛰기




Volumn 206, Issue 1, 2004, Pages 191-209

Large time behavior of the heat kernel

Author keywords

Ground state; Heat kernel; Principal eigenvalue; Recurrence

Indexed keywords


EID: 0347031300     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(03)00110-1     Document Type: Article
Times cited : (35)

References (32)
  • 2
    • 84972545997 scopus 로고
    • Exponential stability of a diffusion equation with absorption
    • W. Arendt, C.J.K. Batty, Exponential stability of a diffusion equation with absorption, Differential Integral Equations 6 (1993) 1009-1024.
    • (1993) Differential Integral Equations , vol.6 , pp. 1009-1024
    • Arendt, W.1    Batty, C.J.K.2
  • 3
    • 0000377165 scopus 로고
    • Non-negative solutions of linear parabolic equations
    • D.G. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968) 607-694.
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , Issue.3 , pp. 607-694
    • Aronson, D.G.1
  • 4
    • 22844455227 scopus 로고    scopus 로고
    • On minimal parabolic functions and time-homogeneous parabolic h-transforms
    • K. Burdzy, T.S. Salisbury, On minimal parabolic functions and time-homogeneous parabolic h-transforms, Trans. Amer. Math. Soc. 351 (1999) 3499-3531.
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 3499-3531
    • Burdzy, K.1    Salisbury, T.S.2
  • 6
    • 84974001919 scopus 로고
    • Modified isoperimetric constants, and large time heat diffusion in Riemannian manifolds
    • I. Chavel, E.A. Feldman, Modified isoperimetric constants, and large time heat diffusion in Riemannian manifolds, Duke Math. J. 64 (1991) 473-499.
    • (1991) Duke Math. J. , vol.64 , pp. 473-499
    • Chavel, I.1    Feldman, E.A.2
  • 7
    • 51249173410 scopus 로고
    • Large time behavior of the heat kernel: The parabolic λ-potential alternative
    • I. Chavel, L. Karp, Large time behavior of the heat kernel: the parabolic λ-potential alternative, Comment. Math. Helv. 66 (1991) 541-556.
    • (1991) Comment. Math. Helv. , vol.66 , pp. 541-556
    • Chavel, I.1    Karp, L.2
  • 8
    • 85030924015 scopus 로고    scopus 로고
    • Asymptotic of the heat kernel in general Benedicks domain
    • preprint
    • P. Collet, S. Martínez, J. San Martín, Asymptotic of the heat kernel in general Benedicks domain, preprint.
    • Collet, P.1    Martínez, S.2    San Martín, J.3
  • 10
    • 0347038911 scopus 로고    scopus 로고
    • Heat kernels on non-compact Riemannian manifolds: A partial survey
    • Univ. Grenoble I, Saint-Martin-d'Hères
    • T. Coulhon, Heat kernels on non-compact Riemannian manifolds: a partial survey, in: Séminaire de Théorie Spectrale et Géométrie, Sémin. Théor. Spectr. Géom, Vol. 15, Univ. Grenoble I, Saint-Martin-d'Hères, 1997, pp. 167-187.
    • (1997) Séminaire de Théorie Spectrale et Géométrie, Sémin. Théor. Spectr. Géom , vol.15 , pp. 167-187
    • Coulhon, T.1
  • 11
    • 0001565149 scopus 로고    scopus 로고
    • On-diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains
    • T. Coulhon, A. Grigor'yan, On-diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains, Duke Math. J. 89 (1997) 133-199.
    • (1997) Duke Math. J. , vol.89 , pp. 133-199
    • Coulhon, T.1    Grigor'yan, A.2
  • 13
    • 51249170233 scopus 로고
    • Heat kernel bounds, conservation of probability and the Feller property
    • E.B. Davies, Heat kernel bounds, conservation of probability and the Feller property, J. Anal. Math. 58 (1992) 99-119.
    • (1992) J. Anal. Math. , vol.58 , pp. 99-119
    • Davies, E.B.1
  • 14
    • 0001563743 scopus 로고    scopus 로고
    • Non-Gaussian aspects of heat kernel behaviour
    • E.B. Davies, Non-Gaussian aspects of heat kernel behaviour, J. London Math. Soc. (2) 55 (1997) 105-125.
    • (1997) J. London Math. Soc. , vol.55 , Issue.2 , pp. 105-125
    • Davies, E.B.1
  • 15
    • 0003370536 scopus 로고
    • Classical Potential Theory and Its Probabilistic Counterpart
    • Springer, New York
    • J.L. Doob, Classical Potential Theory and Its Probabilistic Counterpart, Grundlehren der Mathematischen Wissenschaften, Vol. 262, Springer, New York, 1984.
    • (1984) Grundlehren Der Mathematischen Wissenschaften , vol.262
    • Doob, J.L.1
  • 16
  • 17
    • 0039657135 scopus 로고    scopus 로고
    • Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
    • A. Grigor'yan, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. 36 (1999) 135-249.
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 135-249
    • Grigor'yan, A.1
  • 19
    • 0000738895 scopus 로고    scopus 로고
    • Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
    • K. Ishige, M. Murata, Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001) 171-223.
    • (2001) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.30 , Issue.4 , pp. 171-223
    • Ishige, K.1    Murata, M.2
  • 20
    • 0346251606 scopus 로고    scopus 로고
    • Approach to equilibrium for a forced Burgers equation
    • W. Kirsch, B. Simon, Approach to equilibrium for a forced Burgers equation, J. Evol. Equations 1 (2001) 411-419.
    • (2001) J. Evol. Equations , vol.1 , pp. 411-419
    • Kirsch, W.1    Simon, B.2
  • 21
    • 0037057030 scopus 로고    scopus 로고
    • Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations
    • M. Murata, Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations, J. Funct. Anal. 194 (2002) 53-141.
    • (2002) J. Funct. Anal. , vol.194 , pp. 53-141
    • Murata, M.1
  • 22
    • 0001247391 scopus 로고
    • Large time behavior of the heat kernel and the behavior of the Green function near criticality for nonsymmetric elliptic operators
    • Y. Pinchover, Large time behavior of the heat kernel and the behavior of the Green function near criticality for nonsymmetric elliptic operators, J. Funct. Anal. 104 (1992) 54-70.
    • (1992) J. Funct. Anal. , vol.104 , pp. 54-70
    • Pinchover, Y.1
  • 23
    • 0001416425 scopus 로고
    • 0 -invariant positive harmonic function, a counter example to Stroock's conjecture
    • 0 -invariant positive harmonic function, a counter example to Stroock's conjecture, Comm. Partial Differential Equations 20 (1995) 1831-1846.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 1831-1846
    • Pinchover, Y.1
  • 25
    • 0010763505 scopus 로고
    • Two-sided estimates of the fundamental solutions of second-order parabolic equations and some applications of them
    • F.O. Porper, S.D. Èǐdel'man, Two-sided estimates of the fundamental solutions of second-order parabolic equations and some applications of them, Uspekhi Mat. Nauk 39 (1984) 107-156.
    • (1984) Uspekhi Mat. Nauk , vol.39 , pp. 107-156
    • Porper, F.O.1    Èǐdel'man, S.D.2
  • 27
    • 85016600983 scopus 로고
    • Schrödinger semigroups
    • B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982) 447-526.
    • (1982) Bull. Amer. Math. Soc. , vol.7 , pp. 447-526
    • Simon, B.1
  • 28
    • 84966251687 scopus 로고
    • Large time behavior of the heat kernel: On a theorem of Chavel and Karp
    • B. Simon, Large time behavior of the heat kernel: on a theorem of Chavel and Karp, Proc. Amer. Math. Soc. 118 (1993) 513-514.
    • (1993) Proc. Amer. Math. Soc. , vol.118 , pp. 513-514
    • Simon, B.1
  • 32
    • 0034348893 scopus 로고    scopus 로고
    • Large time behavior of Schrödinger heat kernels and applications
    • Q.S. Zhang, Large time behavior of Schrödinger heat kernels and applications, Comm. Math. Phys. 210 (2000) 371-398.
    • (2000) Comm. Math. Phys. , vol.210 , pp. 371-398
    • Zhang, Q.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.