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1

A Sharp Bound for the Ratio of the First Two Eigenvalues of Dirichlet Laplacians and Extensions

Mark S. Ashbaugh and Rafael D. Benguria

Journal:

Annals of Mathematics

Year:

1992

Language:

english

File:

PDF, 1.83 MB

english, 1992

2

generalization to three dimensions

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

Duke Mathematical Journal

Year:

1995

Language:

english

File:

PDF, 113 KB

english, 1995

3

Isoperimetric bound for $\lambda_3 / \lambda_2$ for the membrane problem

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

Duke Mathematical Journal

Year:

1991

Language:

english

File:

PDF, 676 KB

english, 1991

4

Universal Bounds for the Low Eigenvalues of Neumann Laplacians in N Dimensions

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

SIAM Journal on Mathematical Analysis

Year:

1993

Language:

english

File:

PDF, 1.51 MB

english, 1993

5

Thomas-Fermi-von Weizs�cker equation

Ashbaugh, Mark S., Benguria, Rafael D., Yarur, Cecilia

Journal:

Duke Mathematical Journal

Year:

1991

Language:

english

File:

PDF, 1.44 MB

english, 1991

6

Self-Adjointness of Two-Dimensional Dirac Operators on Domains

Benguria, Rafael D., Fournais, Søren, Stockmeyer, Edgardo, Van Den Bosch, Hanne

Journal:

Annales Henri Poincaré

Year:

2017

Language:

english

File:

PDF, 515 KB

english, 2017

7

Bounds for Ratios of Eigenvalues of the Dirichlet Laplacian

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

Proceedings of the American Mathematical Society

Year:

1994

Language:

english

File:

PDF, 172 KB

english, 1994

8

equations

Benguria, Rafael D., Lorca, Sebasti�n, Yarur, Cecilia S.

Journal:

Duke Mathematical Journal

Year:

1994

Language:

english

File:

PDF, 1.37 MB

english, 1994

9

A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space

Benguria, Rafael D., Linde, Helmut

Journal:

Duke Mathematical Journal

Year:

2007

Language:

english

File:

PDF, 349 KB

english, 2007

10

Classification of the Solutions of Semilinear Elliptic Problems in a Ball

Rafael D. Benguria, Jean Dolbeault, Maria J. Esteban

Journal:

Journal of Differential Equations

Year:

2000

Language:

english

File:

PDF, 289 KB

english, 2000

11

The Brézis–Nirenberg Problem on S3

Catherine Bandle, Rafael Benguria

Journal:

Journal of Differential Equations

Year:

2002

Language:

english

File:

PDF, 172 KB

english, 2002

12

Many-body atomic potentials in Thomas-Fermi theory

Rafael Benguria, Elliott H Lieb

Journal:

Annals of Physics

Year:

1978

Language:

english

File:

PDF, 597 KB

english, 1978

13

Oscillating minimizers of a fourth-order problem invariant under scaling

Rafael D Benguria, Isabelle Catto, Jean Dolbeault, Régis Monneau

Journal:

Journal of Differential Equations

Year:

2004

Language:

english

File:

PDF, 271 KB

english, 2004

14

The Thomas-Fermi-von Weizsäcker theory of atoms and molecules

Rafael Benguria, Haim Brezis, Elliott H. Lieb

Journal:

Communications in Mathematical Physics

Year:

1981

Language:

english

File:

PDF, 735 KB

english, 1981

15

A second proof of the Payne-Pólya-Weinberger conjecture

Mark S. Ashbaugh, Rafael D. Benguria

Journal:

Communications in Mathematical Physics

Year:

1992

Language:

english

File:

PDF, 492 KB

english, 1992

16

A Second Eigenvalue Bound for the Dirichlet Schrödinger Operator

Rafael D. Benguria, Helmut Linde

Journal:

Communications in Mathematical Physics

Year:

2006

Language:

english

File:

PDF, 219 KB

english, 2006

17

More Bounds on Eigenvalue Ratios for Dirichlet Laplacians in N Dimensions

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

SIAM Journal on Mathematical Analysis

Year:

1993

Language:

english

File:

PDF, 3.30 MB

english, 1993

18

Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle

Benguria, Rafael, Lieb, Elliott H.

Journal:

Physical Review Letters

Year:

1983

Language:

english

File:

PDF, 596 KB

english, 1983

19

THE RANGE OF VALUES OF λ 2 /λ 1 AND λ 3 /λ 1 FOR THE FIXED MEMBRANE PROBLEM

ASHBAUGH, MARK S., BENGURIA, RAFAEL D.

Journal:

Reviews in Mathematical Physics

Year:

1994

Language:

english

File:

PDF, 344 KB

english, 1994

20

Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

Proceedings of the Royal Society of Edinburgh Section A Mathematics

Year:

1993

Language:

english

File:

PDF, 473 KB

english, 1993

21

Symmetry Properties of the Solutions to Thomas-Fermi-Dirac-Von Weizsäcker Type Equations

Rafael D. Benguria and Cecilia Yarur

Journal:

Transactions of the American Mathematical Society

Year:

1990

Language:

english

File:

PDF, 1.08 MB

english, 1990

22

Proof of the Payne-Pólya-Weinberger conjecture

Ashbaugh, Mark S., Benguria, Rafael D.

Journal:

Bulletin of the American Mathematical Society

Year:

1991

Language:

english

File:

PDF, 800 KB

english, 1991

23

A Sharp Bound for the Ratio of the First Two Dirichlet Eigenvalues of a Domain in a Hemisphere of Sn

Mark S. Ashbaugh and Rafael D. Benguria

Journal:

Transactions of the American Mathematical Society

Year:

2001

Language:

english

File:

PDF, 4.02 MB

english, 2001

24

Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots

Benguria, Rafael D., Fournais, Søren, Stockmeyer, Edgardo, Van Den Bosch, Hanne

Journal:

Mathematical Physics, Analysis and Geometry

Year:

2017

Language:

english

File:

PDF, 887 KB

english, 2017

25

Existence and non-existence of minimizers for Poincaré–Sobolev inequalities

Benguria, Rafael D., Vallejos, Cristobal, Van Den Bosch, Hanne

Journal:

Calculus of Variations and Partial Differential Equations

Year:

2020

File:

PDF, 501 KB

2020

26

Some eigenvalue inequalities for a class of Jacobi matrices

Mark S. Ashbaugh, Rafael D. Benguria

Journal:

Linear Algebra and its Applications

Year:

1990

Language:

english

File:

PDF, 1.03 MB

english, 1990

27

Some eigenvalue inequalities for a class of Jacobi matrices

Mark S. Ashbaugh, Rafael D. Benguria

Journal:

Linear Algebra and its Applications

Year:

1991

Language:

english

File:

PDF, 35 KB

english, 1991

28

Log-concavity of the ground state of Schrödinger operators: A new proof of the Baumgartner-Grosse-Martin inequality

Mark S. Ashbaugh, Rafael D. Benguria

Journal:

Physics Letters A

Year:

1988

Language:

english

File:

PDF, 243 KB

english, 1988

29

Fourier transform, null variety, and Laplacian's eigenvalues

Rafael Benguria, Michael Levitin, Leonid Parnovski

Journal:

Journal of Functional Analysis

Year:

2009

Language:

english

File:

PDF, 307 KB

english, 2009

30

A new estimate on the indirect Coulomb energy

Rafael D. Benguria, Gonzalo A. Bley, Michael Loss

Journal:

International Journal of Quantum Chemistry

Year:

2012

Language:

english

File:

PDF, 100 KB

english, 2012

31

A lower bound on the size of molecules

Hugo R. Alarcón, Rafael D. Benguria

Journal:

Letters in Mathematical Physics

Year:

1995

Language:

english

File:

PDF, 341 KB

english, 1995

32

Dependence of the Thomas-Fermi energy on the nuclear coordinates

Rafael Benguria

Journal:

Communications in Mathematical Physics

Year:

1981

Language:

english

File:

PDF, 552 KB

english, 1981

33

Existence and uniqueness of positive solutions of semilinear elliptic equations with Coulomb potentials on ℝ3

Rafael Benguria, Lorenzo Jeanneret

Journal:

Communications in Mathematical Physics

Year:

1986

Language:

english

File:

PDF, 893 KB

english, 1986

34

Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials

Mark S. Ashbaugh, Rafael D. Benguria

Journal:

Communications in Mathematical Physics

Year:

1989

Language:

english

File:

PDF, 860 KB

english, 1989

35

Dissociation of Homonuclear Relativistic Molecular Ions

Rafael Benguria, Heinz Siedentop, Edgardo Stockmeyer

Journal:

Annales Henri Poincaré

Year:

2001

Language:

english

File:

PDF, 152 KB

english, 2001

36

Binding Threshold for the Pauli–Fierz Operator

Rafael D. Benguria, Semjon A. Vugalter

Journal:

Letters in Mathematical Physics

Year:

2004

Language:

english

File:

PDF, 106 KB

english, 2004

37

Variational Calculation of the Period of Nonlinear Oscillators

Rafael Benguria, M. Cristina Depassier

Journal:

Journal of Statistical Physics

Year:

2004

Language:

english

File:

PDF, 315 KB

english, 2004

38

Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsäcker model

Benguria, Rafael D., Loss, Michael, Siedentop, Heinz

Journal:

Journal of Mathematical Physics

Year:

2008

Language:

english

File:

PDF, 476 KB

english, 2008

39

Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator

Benguria, Rafael D., Linde, Helmut, Loewe, Benjamín

Journal:

Bulletin of Mathematical Sciences

Year:

2012

Language:

english

File:

PDF, 620 KB

english, 2012

40

Microgravity effects on Drosophila melanogaster behavior and aging. Implications of the IML-2 experiment

Alberto Benguría, Enrique Grande, Emilio De Juan, Cristina Ugalde, Jaime Miquel, Rafael Garesse, Roberto Marco

Journal:

Journal of Biotechnology

Year:

1996

Language:

english

File:

PDF, 963 KB

english, 1996

41

A New Estimate on the Two-Dimensional Indirect Coulomb Energy

Rafael D. Benguria, Pablo Gallegos, Matěj Tušek

Journal:

Annales Henri Poincaré

Year:

2012

Language:

english

File:

PDF, 234 KB

english, 2012

42

Variational principle for the chemical potential in the Thomas-Fermi model

Benguria, Rafael D, Yáñez, Julio M

Journal:

Journal of Physics A: Mathematical and General Physics

Year:

1998

Language:

english

File:

PDF, 141 KB

english, 1998

43

Spectral Analysis of Quantum Hamiltonians ||

Benguria, Rafael, Friedman, Eduardo, Mantoiu, Marius

Year:

2012

Language:

english

File:

PDF, 3.66 MB

english, 2012

44

Spectral Analysis of Quantum Hamiltonians || Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential

Benguria, Rafael, Friedman, Eduardo, Mantoiu, Marius

Year:

2012

Language:

english

File:

PDF, 293 KB

english, 2012

45

Quantum Langevin Equation

Benguria, Rafael, Kac, Mark

Journal:

Physical Review Letters

Year:

1981

Language:

english

File:

PDF, 241 KB

english, 1981

46

-Dimensional Charged Black Hole in Topologically Massive Electrodynamics

Andrade, Tomás, Bañados, Máximo, Benguria, Rafael D., Gomberoff, Andrés

Journal:

Physical Review Letters

Year:

2005

Language:

english

File:

PDF, 86 KB

english, 2005

47

Exact asymptotic behavior of the Pekar–Tomasevich functional

Benguria, Rafael D., Bley, Gonzalo A.

Journal:

Journal of Mathematical Physics

Year:

2011

Language:

english

File:

PDF, 339 KB

english, 2011

48

Upper and lower bounds for eigenvalues of nonlinear elliptic equations: I. The lowest eigenvalue

Benguria, Rafael

Journal:

Journal of Mathematical Physics

Year:

1983

Language:

english

File:

PDF, 454 KB

english, 1983

49

Electrodynamics and the equations of motion for charged particles with spin

Benguria, Rafael

Journal:

Physical Review D

Year:

1976

Language:

english

File:

PDF, 157 KB

english, 1976

50

On the linear stability theory of Bénard–Marangoni convection

Benguria, Rafael D., Depassier, M. Cristina

Journal:

Physics of Fluids A Fluid Dynamics

Year:

1989

Language:

english

File:

PDF, 445 KB

english, 1989