Preprints
89. Pólya-type inequalities on spheres and hemispheres
Ann. Inst. Fourier (Grenoble)
(with Jing Mao
and
Isabel Salavessa).
Published Articles
88. Families of non-tiling domains satisfying Pólya's conjecture
87. Two balls maximize the third Neumann eigenvalue in hyperbolic space
J. Math. Phys.
64 (2023), 121503
(with Isabel Salavessa).
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
XXIII (2022), 1325-1355 (with
Richard S. Laugesen).
86.
Bessel quotients and Robin eigenvalues
Pacific J. Math. 315 (2021), 75-87.
85. Extremal domains and Pólya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles
Int. Math. Res. Not. IMRN
2021, no. 18, 13730–13782
(with James B. Kennedy).
84. From Neumann to Steklov and beyond, via Robin:
the Weinberger way
Amer. J. Math.
143 (2021), 969–994 (with Richard
S. Laugesen).
83.
Optimal unions of scaled copies of domains and Pólya's conjecture
Ark. Math.
59 (2021), 11-51 (with Jean Lagacé and Jordan Payette).
82. A Gelfand-Levitan trace formula for generic quantum graphs
Anal. Math. Phys.
11 (2021), 56, 19 pp.
(with
Jiří Lipovský).
81. The determinant of one-dimensional polyharmonic operators of arbitrary order
J. Funct. Anal.
279 (2020), 108783, 30 pp.
(with
Jiří Lipovský).
80. The damped wave equation with singular damping
Proc. Amer. Math. Soc.
148 (2020), 4273-4284
(with
Nicolas Hefti and
Petr Siegl)
.
79. From Steklov to Neumann and beyond, via Robin: the Szegö way
Canadian J. Math. 72 (2020), 1024-1043
(with Richard S. Laugesen).
78. Maximal determinants of Schrödinger operators on bounded intervals
J. Éc. polytech. Math.
7 (2020), 803-829
(with Clara Aldana and
Jean-Baptiste Caillau).
77. Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles
Proc. Amer. Math. Soc.
148 (2020), 1109-1120
(with Davide Buoso).
76. On the behaviour of clamped plates under large compression
SIAM J. Appl. Math.
79 (2019), 1872-1891
(with
Pedro R.S. Antunes and Davide Buoso).
75. Spectral determinant for the damped wave equation on an interval
Acta Phys. Polon. A
136 (2019), 817-823 (with
Jiří Lipovský).
74.
A remark on Pólya's conjecture at low frequencies
Arch. Math. (Basel) 112 (2019), 305-311.
73.
The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions
Math. Ann. 372 (2018), 1081–1101.
72. The damped wave equation with unbounded damping
J. DIfferential Equations
264 (2018), 7023-7054
(with
Petr Siegl and C. Tretter).
71. Decay of solutions for a class of nonlinear Schrödinger equations in ℝ and the stability of shock profiles for a quasilinear Benney system
Nonlinearity
31 (2018), 1110-1119
(with
João-Paulo Dias).
70. Sharp bounds for the modulus and phase of
Hankel functions with applications to Jaeger integrals
Math. Comp. 87 (2018), 289-308.
69. Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
Adv. Calc. Var.
10 (2017), 357-379
(with
Pedro R.S. Antunes and David Krejčiřík).
68. The spectrum of geodesic balls on spherically symmetric manifolds
Comm. Anal. Geom. 25 (2017), 507-544
(with Denis Borisov).
67. Eigenvalue asymptotics for the damped wave equation on metric graphs
J. Differential Equations 263 (2017), 2780-2811
(with Jiří Lipovský).
66. Asymptotic behaviour of extremal averages of Laplacian eigenvalues
J. Stat. Phys.
167 (2017), 1511-1518.
65. Summation formula inequalities for eigenvalues of Schrödinger operators
J. Spectral Theory
6 (2016), 483-503
(with James B. Kennedy).
64. Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction
Appl. Math. Optimiz.
73 (2016), 313-328
(with
Pedro R.S. Antunes).
63. Summation formula inequalities for eigenvalues of the perturbed
harmonic oscillator
Osaka J. Math.
53 (2016), 397-416
(with James B. Kennedy).
62. Alexandrov's isodiametric conjecture and the cut
locus of a surface
Tohoku Math. J.
67 (2015), 405-417
(with David
Krejčiřík).
61. The first Robin eigenvalue with negative boundary parameter
Adv. Math.
280 (2015), 322-339
(with David
Krejčiřík).
60. Spectra of graphene nanoribbons with armchair and zigzag boundary conditions
Rev. Math. Phys.
26 (2014), 1450018 (32 pages)
(with Petr
Siegl).
59. Optimal ball placement in rugby conversions
SIAM Rev. 56 (2014), 673-690.
58. Spherical symmetrization and the first eigenvalue of geodesic
disks on manifolds
Calc. Var. Partial Differential Equations
51 (2014), 701-724
(with Jing Mao
and
Isabel Salavessa).
57. On the spectrum of deformations of compact double-sided flat hypersurfaces
Anal. PDE 6 (2013), 1051-1088
(with Denis Borisov).
56. Asymptotic behaviour of optimal spectral planar domains with fixed perimeter
J. Math. Phys. 54 (2013), 053504
(with Dorin Bucur).
55. Asymptotic behaviour and
numerical approximation of optimal eigenvalues of the Robin Laplacian
ESAIM: Control, Optimisation and Calculus of Variations
19 (2013), 438-459
(with
Pedro R.S. Antunes and James B. Kennedy).
54. Asymptotics for the expected lifetime of Brownian motion on
thin domains in ℝn
J. Theoret. Probab. 26 (2013), 284-309
(with Denis Borisov).
53. Optimal spectral rectangles and lattice ellipses
Proc. Royal
Soc. A Math. Phys. Eng. Sci. 469 (2013), 20120492
(with
Pedro R.S. Antunes).
52. On the role of spectral markers
and stability in spine models
J. Mech. Behavior Biomed. Materials
14 (2012), 19-28
(with
Pedro R.S. Antunes).
51. Numerical optimization of
low eigenvalues of the Dirichlet and Neumann Laplacians
J. Opt. Theory Appl.
154 (2012), 235-257
(with
Pedro R.S. Antunes).
50. Eigenvalue asymptotics for almost flat compact
hypersurfaces
Dokl. Akad. Nauk. 442 (2012), 151-155;
translation in
Dokl. Math. 85 (2012), 18-22
(with Denis Borisov).
49. Sharp estimates and saturation phenomena for a nonlocal
eigenvalue problem
Adv. Math. 228 (2011), 2352-2365
(with Barbara Brandolini,
Carlo Nitsch
and Cristina Trombetti).
48. On the inverse
spectral problem for Euclidean triangles
Proc. Royal
Soc. A Math. Phys. Eng. Sci. 467 (2011), 1546-1562
(with
Pedro R.S. Antunes).
47. A spectral Bernstein theorem
Ann. Mat. Pura Appl. 190 (2011), 77-90
(with Isabel Salavessa ).
46. Bounds for the first Dirichlet eigenvalue of triangles
and quadrilaterals
ESAIM: Control, Optimisation and Calculus of Variations
16 (2010), 646-676
(with Bartlomjej Siudeja).
45. On the characterization of harmonic and subharmonic
functions via mean-value properties
Potential Anal. 32 (2010), 189-200
(with João Palhoto Matos).
44. Asymptotics of Dirichlet eigenvalues and eigenfunctions
of the Laplacian on thin domains in ℝd
J. Funct. Anal. 258 (2010), 893-912
(with Denis Borisov).
43. On the effect of sharp rises in blood pressure in the
Shah-Humphrey model for intracranial saccular aneurysms
Biomech. Model. Mechanobiology
8 (2009), 457-471.
42. Eigenvalue asymptotics, inverse problems and a trace
formula for the linear damped wave equation
J. Differential Equations 247 (2009), 3028-3039
(with Denis Borisov).
41. Singular asymptotic expansions
for Dirichlet eigenvalues and eigenfunctions on thin planar domains
Ann.
Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 547-560
(with Denis
Borisov).
40. Hearing the weights of weighted
projective planes
Ann.
Global Anal. Geom. 33 (2008), 373-395 (with Miguel
Abreu, Emily
B. Dryden and Leonor Godinho).
39. A sharp upper bound for the
first Dirichlet eigenvalue and the growth of the isoperimetric
constant of convex domains
Proc.
Amer. Math. Soc. 136 (2008), 2997-3006 (with David
Krejčiřík).
38. Location of the nodal set for
thin curved tubes
Indiana
Univ. Math. J. 57 (2008), 343-376 (with David
Krejčiřík).
37. A
numerical study of the spectral gap
J.
Phys. A 41 (2008), 055201 (with Pedro
R.S. Antunes).
36. On
convex surfaces with minimal moment of inertia
J. Math. Phys.
48 (2007), 122902 (with Richard
S. Laugesen and Gerrard
F. Liddell).
35.
Precise bounds and asymptotics for the first Dirichlet eigenvalue of
triangles and rhombi
J. Funct. Anal.
251 (2007), 376-398.
34.
Unbounded planar domains whose second nodal
line does not touch the boundary
Math.
Res. Lett. 14 (2007), 107-111 (with David
Krejčiřík).
33.
Waveguides with combined Dirichlet and Robin
boundary conditions
Math. Phys. Anal.
Geom. 9 (2006), 335-352 (with David
Krejčiřík).
32.
New bounds for the principal Dirichlet eigenvalue of planar regions
Experiment. Math. 15 (2006),
333-342 (with
Pedro
R.S. Antunes).
31. A
Li-type criterion for zero-free half-planes of Riemann's zeta
function
J. London Math. Soc. 73
(2006), 399-414.
30. Upper and
lower bounds for the first Dirichlet eigenvalue of a triangle
Proc. Amer. Math. Soc. 134
(2006), 2083-2089.
29. Extension
of Abel's Lemma with q-series implications
Ramanujan J. 10 (2005), 137-152 (with George
E. Andrews).
28. Geometrically
induced discrete spectrum in curved tubes
Differential Geom. Appl. 23 (2005), 95-105
(with Boris Chenaud, Pierre
Duclos and David
Krejčiřík).
27. Integrals
of polylogarithmic functions, recurrence relations, and associated
Euler sums
Math. Comp. 74
(2005), 1425-1440.
26. Instability
results for the damped wave equation in unbounded domains
J. Differential Equations 211 (2005),
168-186 (with David
Krejčiřík).
25. On
the first twisted Dirichlet eigenvalue
Comm.
Anal. Geom. 12 (2004), 1083-1103 (with
Antoine
Henrot).
24. A lower
bound to the spectral threshold in curved tubes
R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460
(2004), 3457-3467 (with Pavel
Exner and David
Krejčiřík).
23.
Closed nodal lines and interior hot spots of
the second eigenfunction of the Laplacian on surfaces
Indiana Univ. Math. J. 51 (2002), 305-316.
22. Memory
driven instability in a diffusion process
SIAM J. Math. Anal. 33 (2002), 1090-1106 (with
Brian R. Duffy and
Michael
Grinfeld).
21. On the
invariant spectrum of S1-invariant
metrics on S2
Proc. London Math. Soc. 84 (2002), 213-230
(with Miguel
Abreu).
20.
On minimal eigenvalues of Schrödinger
operators on manifolds
Commun. Math.
Phys. 217 (2001), 375-382.
19. Lyapunov
functionals and stability for FitzHugh-Nagumo systems
J. Differential Equations 169 (2001),
208-227 (with Carlos
Rocha).
18. Delay induced instabilities in
gyroscopic systems
SIAM J. Control Optimization 39 (2000), 196-207.
17. Stability of stationary solutions
of nonlocal reaction-diffusion equations in n-dimensional space
Differential and Integral Equations 13
(2000), 265-288 (with Mikhail Vishnevskii).
16.
Spectral sequences for quadratic pencils and
the inverse spectral problem for the damped wave equation
J. Math. Pures Appl. 78 (1999), 965-980.
15. On the optimal value of the
spectral abscissa for a system of linear oscillators
SIAM J. Matrix Anal. Appl. 21 (1999),
195-208 (with Peter
Lancaster).
14. Optimizing
the rate of decay of solutions of the wave equation using genetic
algorithms: a counterexample to the constant damping conjecture
SIAM J. Control
Optimization 37 (1999), 376-387.
13.
Quadratic matrix polynomials with Hamiltonian
spectrum and oscillatory damped systems
Z. Angew. Math. Phys. 50 (1999), 64-81.
12. Nonlocal reaction-diffusion
equations
Differential Equations with Applications to Biology 187-204, Fields
Inst. Commun. 21, Am. Math. Soc. 1999.
11.
Positivity results for a nonlocal elliptic
equation
Proc.
Roy. Soc. Edinburgh 128 (1998), 697-715 (with Guido
Sweers).
10.
The linear wave equation, Hamiltonian
symmetry, and the importance of being odd
Disc. Cont. Dyn. Syst. 4 (1998),
635-640.
9. Eigenvalue problems for the
wave equation with strong damping
Proc. Roy. Soc. Edinburgh A 127 (1997),
755-771.
8. Stability of
finite-dimensional systems with indefinite damping
Adv. Math. Sci. Appl. 7 (1997), 435-446 (with
Michael Grinfeld and Philip
Knight).
7. Some results on the stability and
bifurcation of stationary solutions of delay-diffusion equations
J. Math. Anal. Appl. 206 (1997), 59-82.
6. Stability results for the
wave equation with indefinite damping
J. Differential Equations 132 (1996),
338-352 (with Enrique
Zuazua).
5. On some eigenvalue problems related to the
wave equation with indefinite damping
J.
Differential Equations 127 (1996), 320-335.
4. Stability of stationary solutions of a
nonlocal reaction-diffusion equation
Quart. J. Mech. Appl. Math. 48 (1995),
557-582.
3. Stationary
solutions of an equation modelling ohmic heating
Appl. Math. Lett. 7 (1994), 1-6 (with Michael
Grinfeld).
2. Bifurcation and stability of stationary
solutions of nonlocal scalar reaction-diffusion equations
J. Dynam. Differential Equations 6
(1994), 613-629.
1. A
nonlocal Sturm-Liouville eigenvalue problem
Proc. Roy. Soc. Edinburgh A 124 (1994),
169-188.
Books (as editor, book chapters)
2.
The Robin problem
in
Shape optimization and spectral theory,
2017, 78-119
Antoine Henrot (ed.), De Gruyter.
(with Dorin Bucur
and James B. Kennedy)
1. Topics
in functional differential and difference equations
Fields Inst. Commun.
29, Amer. Math. Soc.,
Providence, RI, 2001 (co-editor: Teresa
Faria).
Proceedings
4. A lower bound to the spectral threshold
in curved quantum layers
Functional Analysis and Operator Theory for Quantum Physics (2017), 261-269
Volume dedicated to Pavel Exner on the occasion of his 70th birthday
J. Dittrich, H.Kovarik, and A. Laptev (eds.), EMS Publishing House
(with David
Krejčiřík).
3. Characterization and parameterization of the singular
manifold of a simple 6–6 Stewart platform
Nonlinear Science and Complexity (2011), 255-262,
J.A.T. Machado et al. eds. (with Tiago Charters).
2. (In)stability results for the wave equation with indefinite damping
Proceedings of Equadiff 95 (1998), 350-355
1. Bogdanov singularity in the FitzHugh-Nagumo equations
Proceedings of Equadiff 91 (1993), 496-500
(with Carlos Rocha).
Reports
12. Modelling percolation and fractal structure in aerogels
92nd European Study Group with Industry
(2013)
(with Adérito Araújo, Joaquim Correia, Michael Grinfeld, Jevgenija Pavlova and
Diogo Pinheiro).
11. Modelling fiber flow in fiberboard manufacturing
86th European Study Group with Industry
(2012)
(with Diogo Pinheiro,
João Penedones
and José Matos).
10. Asymptotic behaviour of some eigenvalue optimisation problems
Oberwolfach report no. 33/2012.
9. Balanced Scorecard
81st European Study Group with Industry
(2011)
(with Elisete Correia and Irene Oliveira).
8. Detecting singularities of Stewart platforms
Mathematics-in-Industry Case Studies 1 (2009), 66-80 Fields Institute Publications
(with Tiago Charters and Ricardo Enguiça).
7. Fraud detection in plastic card operations
69th European Study Group with Industry
(2009)
(with Paulo C.
Aguiar and António J. Rodrigues).
6. Approximating low eigenvalues of the Laplacian:
analysis, geometry and numerics
Oberwolfach report no. 06/2009.
5. Scheduling in a factory
65th European Study Group with Industry
(2008)
(with Jorge Orestes Cerdeira, Tiago Charters, Manuel Cruz and Paulo Vasconcelos).
4. Electrostatic separation of rubber and textiles
65th European Study Group with Industry
(2008).
3. Cooling of a rotor
65th European Study Group with Industry
(2008)
(with Nuno Lopes).
2. Stewart platform
60th European Study Group with Industry (2007)
(with Tiago Charters
and Ricardo Enguiça).
1. Sharp dynamic bounds for eigenvalues of the
Laplacian
Oberwolfach report no. 18/2007.
Other
2.
European Study Groups with Industry at 40 years
SIAM News, March 2009.
1.
European Study Groups with Industry in Portugal:
importing a forty year old concept
CIM Bulletin, December 2008.