| PUBLICACIONES RAFAEL D. BENGURIA |
155. R.D. Benguria, M.C. Depassier, and S. Rica, Variational estimates for the speed propagation of fronts in a nonlinear diffusive Fisher equation, submitted (2022).
138. R. D. Benguria and M. C. Depassier, Reaction diffusion dynamics and the Schryer-Walker solution for domain walls of the Landau-Lifshitz-Gilbert equation, Physical Review B 93, 144416 (2016).
137. R. D. Benguria, Maxwell 150: a celebration in the International Year of Light, International Association of Mathematical Physics, News Bulletin, October 2015 issue, pp. 19-33.128. R. D. Benguria, and Matej Tusek,
Indirect Coulomb energy for two-dimensional atoms, J. Math. Phys. 53, 095213
(2012).
112. R.D. Benguria and H. Linde,
Isoperimetric Inequalities for Eigenvalues of the
Laplace Operator,
in Fourth Summer School in Analysis
and Mathematical Physics:
Topics in Spectral Theory and Quantum Mechanics,
May 2005, Universidad Nacional
Autónoma de México, Inst. Math. Phys, Cuernavaca, México,
Contemporary
Mathematics 476, 1-40 (2008)
111. R.D. Benguria, M.C. Depassier, and M. Loss,
Upper and lower bounds for the speed of pulled fronts
with a cut-off,
European Physical Journal B 61,
331--334 (2008).
110.
R. D. Benguria, M. Loss, and H. Siedentop,
Stability of atoms and
molecules in an ultrarelativistic Thomas-Fermi-Weizsäcker model,
Journal of Mathematical Physics 49, 012302
(7) (2008).
109. R. D. Benguria,
R. Frank, and M. Loss,
The sharp constant in the Hardy-Sobolev-Maz’ya
inequality in the three dimensional upper half plane,
Mathematical Research Letters, 15,
613-622 (2008).
108. R. D. Benguria,
M. C. Depassier, V. Haikala,
The effect of a cutoff on pushed and bistable fronts
of the reaction difusion equation,
Physical Review E 76, 051101
(3) (2007).
107. R.D. Benguria,
and H. Linde,
A second eigenvalue
bound for the Dirichlet Laplacian in
hyperbolic space,
Duke Mathematical Journal 140,
245-279
(2007).
105. M. S. Ashbaugh,
y R. D. Benguria,
Isoperimetric
Inequalities for Eigenvalues of the
Laplacian,
in Spectral Theory and Mathematical
Physics: A Festschrift
in Honor of Barry Simon's 60th Birthday,
(F. Gesztesy, P. Deift, C. Galvez, P. Perry,
and W. Schlag, Eds.)
Proceedings of Symposia in Pure
Mathematics 76, Part 1,
pp. 105-139, Amer. Math. Soc. (Providence, RI) 2007.
104.
Speed of pulled fronts with a cutoff,
Physical Review
E 75, 051106 (5) (2007).
103. R.D. Benguria,
and H. Linde,
A second eigenvalue bound for the Dirichlet
Schrödinger
operator,
Communications in Mathematical Physics 267,
741-755 (2006).
102. R. D. Benguria,
A nonlinear fourth-order minimization problem,
Contemporary Mathematics 412,
79-86 (2006).
101. R. D. Benguria,
R. Brummelhuis, P. Duclos, S. Pérez-Oyarzún, y P. Vytras,
Asymptotic
behaviour of the equilibrium nuclear separation for the H2+ molecule
in a strong magnetic field,
Journal of Physics A: Mathematical
and General 39,
8451 - 8459 (2006).
100. R. D. Benguria,
R. Brummelhuis, P. Duclos, S. Pérez-Oyarzún, and P. Vytras,
Non-relativistic H2+ molecule in a strong magnetic field,
Few Body
Systems 38, 133-137
(2006).
99. A. Reisenegger,
J. Prieto, R. D. Benguria, Dong Lai, P. Araya,
Magnetic Field in
Neutron Stars: A Theoretical Perspective,
in Magnetic Fields in the Universe:
from
Laboratory and Stars to Primordial Structures,
Angra dos Reis, Brazil,
Nov 28 - Dec 3, 2004, (E. M. de Gouveia dal Pino, A. Lazarian, & G.
Lugones, Eds.),
AIP Conference Proceedings 784,
pp. 263-273 (2005).
98. R. D.
Benguria,
and M. Cristina Depassier,
On the transition from pulled to pushed monotonic
fronts of the extended Fisher-Kolmogorov equation,
Physica A 356, 61-65
(2005).
97. T. Andrade, M.
Bañados , R.D. Benguria, and A. Gomberoff,
(2+1)-Dimensional Charged Black
Hole in Topologically Massive Electrodynamics,
Physical Review Letters 95,
021102 (4) (2005).
96. R.D. Benguria,
and M. Cristina Depassier,
On the principal
bifurcation branch of a third-order nonlinear long-wave equation,
Journal of Physics A: Mathematical
and General 38,
2043-2053 (2005).
94. J. Asch, R.D.
Benguria, and P. Stovicek,
Asymptotic properties of the differential equation
h3(h"+h')=1,
Asymptotic Analysis 41,
23- 40 (2005).
93. R.D. Benguria and
Bounding threshold for the Pauli--Fierz operator,
Letters in Mathematical Physics 70,
249 - 257 (2004).
92. R. D. Benguria,
I. Catto, J. Dolbeault and R. Monneau,
Oscillating minimizers of
a fourth order problem invariant under scaling,
Journal of Differential
Equations, 205, 253-269
(2004).
91. R. D. Benguria,
and Michael Loss,
Connection between the Lieb--Thirring conjecture for
Schrödinger operators and an isoperimetric problem for ovals on the
plane, in Partial Differential Equations and
Inverse Problems, C.
Conca, R. Manásevich, G. Uhlmann, and M.S. Vogelius (Eds.),
Comtemporary
Mathematics, 362, Amer.
Math. Soc.,
90. R. D.
Benguria,
and M. C. Depassier,
Variational Calculation of the Period of Nonlinear
Oscillators,
Journal of Statistical Physics, 116,
923-931 (2004).
89. R. D. Benguria,
R. Brummelhuis, P. Duclos, and S. Pérez-Oyarzún,
H2+ in a strong
magnetic field described via an exact solvable model,
Journal of Physics
B: Atomic, Molecular and Optical Physics 37, 2311-2320 (2004).
87. R.D. Benguria,
The Lane-Emden equation revisited,
Contemporary Mathematics 327,
11-19 (2003).
86. R.D. Benguria,
M.C. Depassier,
Linear and marginal stability for fronts of hyperbolic
reaction-diffusion equations,
Physical Review E 66,
26607(6) (2002).
85. R.D. Benguria and
S.
Pérez-Oyarzún,
The ultrarelativistic Thomas-Fermi model,
Journal
of Physics A: Mathematical and General 35,
3409-3414 (2002).
84. C.Bandle, R.D.
Benguria,
The Brézis-Nirenberg Problem on S³,
Journal of Differential
Equations, 178 , 264 - 279
(2002).
83. R.D. Benguria,
Rayleigh-Faber-Krahn Inequality,
in Encyclopaedia of Mathematics,
Supplement III, Managing Editor: M. Hazewinkel,
Kluwer Academic Publishers, pp. 325-327, (2001).
82. R.D. Benguria,
Neumann Eigenvalue,
in Encyclopaedia of Mathematics,
Supplement III, Managing Editor: M. Hazewinkel,
Kluwer Academic Publishers, pp. 280-281, (2001).
81. R.D. Benguria,
Dirichlet Eigenvalue,
in Encyclopaedia of Mathematics,
Supplement III, Managing Editor: M. Hazewinkel,
Kluwer Academic Publishers, pp. 130-132, (2001).
80. R.D. Benguria, H.
Siedentop,
and E. Stockmeyer,
Dissociation of homonuclear relativistic molecular ions,
Annales Henri Poincaré 2, 27-
40 (2001).
79. M. S. Ashbaugh
and R. D. Benguria,
A Sharp Bound for the Ratio of the First Two Dirichlet
Eigenvalues of a Domain in a Hemisphere of Sn,
Transactions of the American Mathematical Society 353, 1055-1087 (2001).
75. R. D. Benguria
and M. Loss,
A simple proof of a theorem of Laptev and Weidl,
Mathematical Research Letters 7,
195-203 (2000).
74. R. D. Benguria
and M. C.Depassier,
A Reversed Poincaré Inequality for Monotone Functions,
Journal of Inequalities and Applications 5, 91-96 (2000).
73. R.D. Benguria and
M.C.
Depassier,
Variational principle for the limit cycle of
Rayleigh's equation,
in Differential Equations and
Mathematical Physics, (R. Weikard and
G. Weinstein, Eds.),
Studies in Advanced Mathematics, 16,
21-26
(2000).
72. H. Alarcón,
R. D. Benguria, P. Duclos, and H. Hogreve,
On the Stability of Positive Molecular Ions,
Helvetica Physica Acta 72,
386-407 (1999).
71. R. D. Benguria
and M. C.Depassier,
Variational principle for limit cycles of the Rayleigh-van der Pol
equation,
Physical Review E 59,
4889-4893 (1999).
70. R. D. Benguria,
M. C. Depassier, and M. Favre,
Problemas Resueltos de Electricidad y Magnetismo,
Ediciones, Universidad Católica de Chile, Santiago de Chile, 1998.
ISBN 956-14-0514-8
(Segunda Edición, Santiago de Chile, 2004, Tercera Edición, Santiago de
Chile 2008).
69. R. D. Benguria
and M. C. Depassier,
A Variational Method for Nonlinear Eigenvalue Problems,
in Advances in Differential Equations
and Mathematical Physics, (Eric Carlen, Evans Harrell, and
Michael Loss, Eds.),
Amer. Math. Soc., Contemporary Mathematics, 217, 1-17 (1998).
68. R. D. Benguria
and M. C.Depassier,
Speed of fronts of generalized reaction-diffusion equations,
Physical Review E 57,
6493-6496 (1998).
67. R. D. Benguria
and M. C. Depassier,
Phase Space Derivation of a Variational Principle for
One-dimensional Hamiltonian Systems,
Physics Letters A 240, 144-146
(1998).
66. R. D. Benguria
and J. M. Yáñez,
Variational Principle for the Chemical Potential
in the Thomas-Fermi Model,
Journal of Physics A: Mathematical and General
31, 585-593 (1998).
65. M. S. Ashbaugh
and R. D. Benguria,
On the Payne-Pólya-Weinberger
conjecture on the n-dimensional sphere,
in General Inequalities 7, (C.
Bandle , W. N. Everitt, L. Losonczi, and W. Walter, Eds.),
International Series of Numerical Mathematics, 123, pp. 111-128, Birkhäuser Verlag
(Basel) 1997.
64. M. S. Ashbaugh,
R. D. Benguria, and R. S. Laugesen,
Inequalities for the first
eigenvalues of the clamped plate and buckling problems,
in General Inequalities 7, (C.
Bandle , W. N. Everitt, L. Losonczi, and W. Walter, Eds.),
International Series of Numerical Mathematics, 123, pp. 95-110, Birkhäuser Verlag
(Basel) 1997.
63. R. D. Benguria
and M.C . Depassier,
Problemas Resueltos de Mecánica Clásica,
Ediciones Universidad Católica de Chile, Santiago de Chile, 1996.
ISBN 956-14-0403-6.
(Segunda Edición, publicada por Alfaomega Grupo
Editor, México, D.F., 1999. ISBN 970-15-0426-7) .
62. R. D. Benguria
and M. C. Depassier,
Monotonic Fronts of the Reaction-Diffusion Equation in One Space
Dimension,
in Instabilities and Nonequilibrium
Structures V, (E. Tirapegui and W. Zeller, Eds.),
Kluwer Academic Publishers, Dordrecht, pp. 105-110, 1996.
61. R. D. Benguria
and M. C. Depassier,
A variational principle for eigenvalue problems of
Hamiltonian systems,
Physical Review Letters 77,
2847-2850 (1996).
60. R. D. Benguria
and M. C. Depassier,
Speed of fronts of the reaction-diffusion equation,
Physical Review Letters 77,
1171-1173 (1996).
59. M. S. Ashbaugh
and R. D. Benguria,
Bounds for Ratios of the First, Second, and Third Membrane Eigenvalues,
in Nonlinear Problems in Applied
Mathematics, in honor of Ivar Stakgold on his 70th birthday,
(T.S. Angell, L. P. Cook, R.E. Kleinman y W.E. Olmstead, Eds.), SIAM,
Philadelphia, pp. 30-42, 1996.
58. R. D. Benguria,
and M. C. Depassier,
Variational Characterization of the Speed of
Propagation of Fronts for the Nonlinear Diffusion Equation,
Communications in Mathematical Physics, 175, 221- 227 (1996).
57. R. D.
Benguria, J. Cisternas, and M. C. Depassier,
Variational Calculations for Thermal Combustion Waves,
Physical Review E 52, 4410 –
4413 (1995).
56. R. D. Benguria
and M. C. Depassier,
A Variational Principle for the Asymptotic Speed of
Fronts of the
Physical Review E 52,
3285-3287 (1995).
55. R. D. Benguria, and M. C. Depassier,
Monotonic Fronts in Phase Space, in Differential Equations and
Mathematical Physics,
in Differential Equations and
Mathematical Physics,
Proceedings of the International Conference, Univ. Alabama at Birmingham,
March 13-17, 1994, (I. W. Knowles, Ed.), pp. 28-36, International Press
(Cambridge, Mass.) 1995.
54. M.S. Ashbaugh,
and R.D. Benguria,
On Rayleigh's Conjecture for the Clamped Plate and its Generalization
to Three Dimensions,
in Differential Equations and
Mathematical Physics,
Proceedings of the International Conference, Univ. Alabama at Birmingham,
March 13-17, 1994, (I. W. Knowles, Ed.),
pp. 17-27, International Press (Cambridge, Mass.) 1995.
53. H. Alarcón
and R. D. Benguria,
A Lower Bound on the Size of Molecules,
Letters in Mathematical Physics 35,
281-289 (1995).
52. M. S. Ashbaugh
and R. D. Benguria,
Sharp Upper Bound to the First Nonzero Neumann
Eigenvalue for Bounded Domains in Spaces of Constant Curvature,
Journal of the London Mathematical Society (2) 52, 402-416 (1995).
51. M. S. Ashbaugh
and R. D. Benguria,
On Rayleigh's Conjecture for the
Clamped Plate and its Generalization to Three Dimensions,
Duke Mathematical Journal 78,
1- 17 (1995).
50. R. D.
Benguria,
Sobre la solución de ecuaciones algebraicas,
Revista del Profesor de Matemáticas, 1, 74-82 (1994).
"On the Solution of Algebraic Equations", translated from the original Spanish version by Mariah Laugesen,
Urbana, Illinois, 2019.
49. M. S. Ashbaugh
and R.D . Benguria,
¿Se puede escuchar la forma de un
tambor?,
Gaceta
de la Sociedad Matemática de Chile, 7-20 (1994).
48. R. D. Benguria
and M. C. Depassier,
Exact fronts for the nonlinear diffusion equation with
quintic nonlinearities,
Physical Review E 50,
3701--3704 (1994).
47. R. D. Benguria
and M. C. Depassier,
On the validity of the linear speed selection
mechanism for fronts
Physical Review Letters 73,
2272-2274 (1994).
46. M. S. Ashbaugh and R. D. Benguria,
The Range of Values of l3 / l1 and l2 / l1
for the Fixed Membrane Problem,
Reviews in Mathematical Physics, 6,
999-1009 (1994).
Reprinted in The State of
Advances Series in Mathematical Physics 20, pp. 167-182, World Scientific (
45. M. S. Ashbaugh
and R.D. Benguria,
Isoperimetric Inequalities for Eigenvalue Ratios,
in Partial Differential Equations
of Elliptic Type, (A. Alvino, E. Fabes, G. Talenti, Eds.)
Symposia Mathematica XXXV,
pp. 1-36, Cambridge University Press (
44. R. D. Benguria, S.
Lorca,
and C. Yarur,
Nonexistence Results for Solutions of Semilinear Elliptic Equations,
Duke Mathematical Journal 74,
615-634 (1994).
41. C. M. Alfaro, R.
D. Benguria, and M. C. Depassier,
The Role of Dispersion in the Generalized Kuramoto-Sivashinsky Equation,
in Instabilities and Nonlinear
Structures. IV, (E. Tirapegui and
Mathematics and Its Applications 267,
40. M. S. Ashbaugh
and R. D. Benguria,
Isoperimetric Bounds for Higher Eigenvalue Ratios for the N-dimensional
Fixed Membrane Problem,
Proceedings of The Royal Society of Edinburgh 123A, 977-985 (1993).
39. M. S. Ashbaugh
and R.D. Benguria,
More Bounds on Eigenvalue Ratios for
Dirichlet Laplacians in N Dimensions,
SIAM Journal of Mathematical Analysis 24, 1622-1651 (1993).
38. M. S. Ashbaugh
and R. D. Benguria,
Universal Bounds for the Low Eigenvalues of Neumann Laplacians in N
Dimensions,
SIAM Journal of Mathematical Analysis 24,
557- 570 (1993).
37. M. S. Ashbaugh
and R. D. Benguria,
Eigenvalue Ratios for Sturm-Liouville Operators,
Journal of Differential Equations 103,
205- 219 (1993).
36. C. M. Alfaro, R.
D. Benguria, and M. C. Depassier,
Finite Mode Analysis of the Kuramoto-Sivashinsky Equation Modified by
Dispersion,
Physica D 61, 1-5 (1992).
35. R. D. Benguria,
S. Hoops, and H. Siedentop,
Bounds on the excess charge and the ionization energy for the
Hellmann-Weizsäcker model,
Annales de l’Institut Henri Poincaré (A) Physique Théorique 57, 47- 65 (1992).
34. M. S. Ashbaugh
and R. D. Benguria,
A Second Proof of
the Payne-Pólya-Weinberger Conjecture,
Communications in Mathematical Physics 147, 181-190 (1992).
33. R. D. Benguria
and M. C. Depassier,
Three mode truncation of a model equation for systems with long wave
oscillatory instability,
Physical Review A 45,
5566-5571 (1992).
29. M. S. Ashbaugh,
R. D. Benguria, and C. Yarur,
Properties of the positive solution of a
generalized Thomas-Fermi-von Weizsäcker equation,
Duke Mathematical
Journal 63, 199-215 (1991).
27. M. S. Ashbaugh
and R. D. Benguria,
Some Eigenvalue Inequalities for a Class of Jacobi Matrices,
Linear Algebra and its Applications 136,
215-234 (1990);
Addendum, Linear Algebra and
its Applications 149, 277
(1991).
26. R.D. Benguria and
C.Yarur,
Symmetry Properties of the solutions to Thomas-Fermi-von Weizsäcker
type equations,
Transactions of the American Mathematical Society 320, 665-675 (1990).
25. R. D. Benguria
and M. C. Depassier,
Oscillatory
Instabilities in BénardMarangoni Convection in a Fluid Bounded Above by
a Free Surface,
in Instabilities and
Nonlinear Structures II: Dynamical Systems and Instabilities, (E.
Tirapegui and D. Villaroel, Eds.),
Mathematics and Its Applications 50,
pp. 221-225, Kluwer Ac. Pub. (
24. R. D. Benguria
and M. C. Depassier,
Equations of the
Korteweg-de Vries type with nontrivial conserved quantities,
Journal of Physics A: Mathematical and General 22, 4135-4142 (1989).
22. R. D. Benguria
and M. C. Depassier,
On the linear
stability theory of Bénard-Marangoni
convection,
Physics of Fluids A 1,
1123-1127 (1989).
19. M. S. Ashbaugh
and R. D. Benguria,
Log-Concavity of the
Ground State of Schrödinger Operators: A New Proof of the Baumgartner,
Grosse, Martin Inequality,
Physics
Letters A 131, 273-276 (1988).
17. R. D. Benguria
and M. C. Depassier,
Oscillatory Instabilities in the Rayleigh-Bénard
Problem with a Free Surface,
Physics of Fluids 30,
1678-1682 (1987).
15. R. D. Benguria
and L. Jeanneret,
Existence and
Uniqueness of Positive Solutions of Semilinear Elliptic Equations with
Coulomb Potentials on R3,
Communications in
Mathematical Physics 104,
291-306 (1986).
A Note
on the Gap Between the first two Eigenvalues for the Schrödinger
Operator,
Journal of Physics A: Mathematical & General 19, 477-478 (1986).
8. R. Benguria and M.
Kac,
Quantum Langevin Equation,
Physical Review Letters 46,
1-4 (1981).
7. D. Levi and R.
Benguria,
Backlund
Transformations and Nonlinear Differential-Difference Equations,
Proceedings of the National
6. R. Benguria and K.
M. Case,
Backlund Transformations for Multi-dimensional
Sine-Gordon Equations,
Proceedings of the National
Remark: The
articles numbers [4], [5], [9], [12] and [13] of the above
list have been reprinted in: The Stability of Matter: From Atoms to
Stars,
Selecta of Elliott H. Lieb, Edited by W. Thirring, Springer-Verlag (NY)
(1991).