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On the principal eigenvalues of some elliptic problems with large drift
1. | FaMAF, Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba, Argentina, Argentina |
2. | Departement de Mathematique, C.P. 214, Universite Libre de Bruxelles, 1050 Bruxelles, Belgium |
References:
[1] |
H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.
doi: 10.1007/s00220-004-1201-9. |
[2] |
H. Berestycki, L. Nirenberg and S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math., 47 (1994), 47-92.
doi: 10.1002/cpa.3160470105. |
[3] |
X. Chen and Y. Lou, Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model, Indiana Univ. Math. J., 57 (2008), 627-658.
doi: 10.1512/iumj.2008.57.3204. |
[4] |
E. N. Dancer, Some remarks on classical problems and fine properties of Sobolev spaces, Diff. Int. Equat., 9 (1996), 437-446. |
[5] |
A. Devinatz, R. Ellis and A. Friedman, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivative II, Indiana Univ. Math. J., 23 (1974), 991-1011. |
[6] |
M. Donsker and S. Varadhan, On the principal eigenvalue of second order differential operators, Comm. Pure Appl. Math., 29 (1976), 595-621.
doi: 10.1002/cpa.3160290606. |
[7] |
J. Fleckinger, J. Hernandez and F. de Thelin, Existence of multiple eigenvalues for some indefinite linear eigenvalue problems, Bolletino U. M. I., 7 (2004), 159-188. |
[8] |
A. Friedman, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivative, Indiana Univ. Math. J., 22 (1973), 1005-1015. |
[9] |
T. Godoy, J. P. Gossez and S. Paczka, A minimax formula for principal eigenvalues and application to an antimaximum principle, Calculus of Variations and Partial Differential Equations, 21 (2004), 85-111.
doi: 10.1007/s00526-003-0249-2. |
[10] |
T. Godoy, J. P. Gossez and S. Paczka, A minimax formula for the principal eigenvalues of Dirichlet problems and its applications, 2006 International Conference in honor of JacquelineFleckinger, Electronic Journal of Differential Equations, Conference, 15 (2007), 137-154. |
[11] |
T. Godoy, J. P. Gossez and S. Paczka, On the asymptotic behavior of the principal eigenvalues of some elliptic problems, Annali di Matematica Pura ed Applicata, 189 (2009), 497-521.
doi: 10.1007/s10231-009-0120-y. |
[12] |
P. Hess, "Periodic-parabolic Boundary Value Problems and Positivity," Pitman, 1991. |
[13] |
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Part. Diff. Equat., 5 (1980), 999-1030.
doi: 10.1080/03605308008820162. |
[14] |
C. Holland, A minimum principle for the principal eigenvalue for second order linear elliptic equation with natural boundary condition, Comm. Pure Appl. Math., 31 (1978), 509-519.
doi: 10.1002/cpa.3160310406. |
[15] |
T. Kato, Superconvexity of the spectral radius, and convexity of the spectral bound and the type, Math. Z., 180 (1982), 265-273.
doi: 10.1007/BF01318910. |
[16] |
J. Lopez Gomez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Diff. Equat., 127 (1996), 263-294.
doi: 10.1006/jdeq.1996.0070. |
[17] |
S. Paczka, A Neumann periodic parabolic eigenvalue problem with continuous weight, Rendiconti del Seminario Matematico dellUniversita e Politecnico di Torino, 54 (1996), 67-74 |
[18] |
S. Timbo, M. Kimura and H. Notsu, Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type, Asymptotic Analysis, 65 (2009), 103-123. |
show all references
References:
[1] |
H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.
doi: 10.1007/s00220-004-1201-9. |
[2] |
H. Berestycki, L. Nirenberg and S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math., 47 (1994), 47-92.
doi: 10.1002/cpa.3160470105. |
[3] |
X. Chen and Y. Lou, Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model, Indiana Univ. Math. J., 57 (2008), 627-658.
doi: 10.1512/iumj.2008.57.3204. |
[4] |
E. N. Dancer, Some remarks on classical problems and fine properties of Sobolev spaces, Diff. Int. Equat., 9 (1996), 437-446. |
[5] |
A. Devinatz, R. Ellis and A. Friedman, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivative II, Indiana Univ. Math. J., 23 (1974), 991-1011. |
[6] |
M. Donsker and S. Varadhan, On the principal eigenvalue of second order differential operators, Comm. Pure Appl. Math., 29 (1976), 595-621.
doi: 10.1002/cpa.3160290606. |
[7] |
J. Fleckinger, J. Hernandez and F. de Thelin, Existence of multiple eigenvalues for some indefinite linear eigenvalue problems, Bolletino U. M. I., 7 (2004), 159-188. |
[8] |
A. Friedman, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivative, Indiana Univ. Math. J., 22 (1973), 1005-1015. |
[9] |
T. Godoy, J. P. Gossez and S. Paczka, A minimax formula for principal eigenvalues and application to an antimaximum principle, Calculus of Variations and Partial Differential Equations, 21 (2004), 85-111.
doi: 10.1007/s00526-003-0249-2. |
[10] |
T. Godoy, J. P. Gossez and S. Paczka, A minimax formula for the principal eigenvalues of Dirichlet problems and its applications, 2006 International Conference in honor of JacquelineFleckinger, Electronic Journal of Differential Equations, Conference, 15 (2007), 137-154. |
[11] |
T. Godoy, J. P. Gossez and S. Paczka, On the asymptotic behavior of the principal eigenvalues of some elliptic problems, Annali di Matematica Pura ed Applicata, 189 (2009), 497-521.
doi: 10.1007/s10231-009-0120-y. |
[12] |
P. Hess, "Periodic-parabolic Boundary Value Problems and Positivity," Pitman, 1991. |
[13] |
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Part. Diff. Equat., 5 (1980), 999-1030.
doi: 10.1080/03605308008820162. |
[14] |
C. Holland, A minimum principle for the principal eigenvalue for second order linear elliptic equation with natural boundary condition, Comm. Pure Appl. Math., 31 (1978), 509-519.
doi: 10.1002/cpa.3160310406. |
[15] |
T. Kato, Superconvexity of the spectral radius, and convexity of the spectral bound and the type, Math. Z., 180 (1982), 265-273.
doi: 10.1007/BF01318910. |
[16] |
J. Lopez Gomez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Diff. Equat., 127 (1996), 263-294.
doi: 10.1006/jdeq.1996.0070. |
[17] |
S. Paczka, A Neumann periodic parabolic eigenvalue problem with continuous weight, Rendiconti del Seminario Matematico dellUniversita e Politecnico di Torino, 54 (1996), 67-74 |
[18] |
S. Timbo, M. Kimura and H. Notsu, Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type, Asymptotic Analysis, 65 (2009), 103-123. |
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