Publications within the scope of this project:
Preprints
48.
P.R.S. Antunes
Extremal p-Laplacian eigenvalues
Nonlinearity
47.
D. Buoso
and
P. Freitas
Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles
Proc. Amer. Math. Soc.
46.
P. Freitas
and
J.B. Kennedy
Extremal domains and Pólya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles
Int. Math. Res. Not. IMRN
45.
J.B. Kennedy
A family of diameter-based eigenvalue bounds for quantum graphs
Discrete and Continuous Models in the Theory of Networks,
Operator Theory: Advances and Applications,
Birkhäuser 2019, F. Atay, P. Kurasov and D. Mugnolo (eds),
44.
P. Freitas and R.S. Laugesen
From Steklov to Neumann and beyond, via Robin:
the Szegö way
Canadian J. Math.
43.
D.
Krejčiřík, V. Lotoreichik and T. Ourmieres-Bonafos
Spectral transitions for Aharonov-Bohm Laplacians on conical layers
Proc. Roy. Soc. Edinburgh Sect. A.
Published Articles
42.
G. Berkolaiko, J.B. Kennedy P. Kurasov and D. Mugnolo,
Surgery principles for the spectral analysis of quantum graphs
Trans. Amer. Math. Soc.
372 (2019), 5153--5197
41.
P.R.S. Antunes,
D. Buoso
and
P. Freitas
On the behaviour of clamped plates under large compression
SIAM J. Appl. Math. 79 (2019), 1872-1891.
40.
F. Della Pietra, N. Gavitone and
G. Piscitelli
On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
Bull. Sci. Math. 155 (2019), 10-32.
39.
N. C. Dias and
J. Prata
A refinement of the Robertson-Schrödinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions
J. Fourier Anal. Appl.
25 (2019), 210-241.
38. C.J.S.Alves and
P.R.S. Antunes
Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions
Engineering Analysis with Boundary Elements
101 (2019), 330-342.
37.
N. C. Dias and
J. Prata
Quantum mappings acting by coordinate transformations on Wigner distributions
Rev. Mat. Iberoamericana
35 (2019), 317–337.
36.
P. Freitas
A remark on Pólya's conjecture at low frequencies
Arch. Math. (Basel)
112 (2019), 305-311.
35.
J.S. Ben-Benjamin,
N. C. Dias, L. Cohen, P. Loughlin, and
J. Prata
What is the Wigner function closest to a given square integrable function?
SIAM J. Math. Anal.
50 (2018), 5161–5197.
34.
C. Aldana and J. Rowlett
A Polyakov formula for sectors
J. Geom. Anal.
28 (2018), 1773–1839.
33.
B. Kawohl and D.
Krejčiřík
From Symmetry to Monotonicity
Math. Intell.
40 (2018), 12-13.
32.
D.
Krejčiřík and R. Tiedra de Aldecoa
Ruled strips with asymptotically diverging twisting
Ann. Henri Poincaré
19 (2018), 2069-2086.
31.
P.R.S. Antunes and F. Gazzola
Some solutions of minimaxmax problems for the torsional displacements of rectangular plates
Z Angew Math Mech. 98 (2018), 1974-1991.
30.
P.R.S. Antunes
A numerical algorithm to reduce the ill conditioning in meshless methods for the Helmholtz equation
Numer. Algorithms 79 (2018), 879-897
29.
P. Freitas
The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions
Math. Ann.
372 (2018), 1081–1101
28.
N. C. Dias and
J. Prata
Wigner functions on non-standard symplectic vector spaces
J. Math. Phys.
59 (2018), 012108.
27.
W. Kirsch, D.
Krejčiřík and G. Raikov
Lifshits tails for randomly twisted quantum waveguides
J. Stat. Phys.
171 (2018), 383-399.
26.
D.
Krejčiřík, N. Raymond, J. Royer and P. Siegl
Reduction of dimension as a consequence of norm-resolvent convergence and applications
Mathematika
64 (2018), 406-429.
25.
C.J.S. Alves and
P.R.S. Antunes,
The Method of Fundamental Solutions applied to boundary value problems on the surface of a sphere
Comput. Math. Appl.
75 (2018), 2365-2373.
24.
P.R.S. Antunes
Reducing the ill conditioning in the Method of Fundamental Solutions
Adv. Comput. Math.
44 (2018), 351-365.
23.
P.R.S. Antunes,
S. A. Mohammadi and
H. Voss
A nonlinear eigenvalue optimization problem: optimal potential functions
Nonlinear Analysis Series B: Real World Applications
46 (2018), 307-327.
22.
P. Freitas,
P. Siegl and
C. Tretter
The damped wave equation with unbounded damping
J. Differential Eq.
264 (2018), 7023-7054.
21.
D.
Krejčiřík and V. Lotoreichik
Optimisation of the lowest Robin eigenvalue in the exterior of a compact set
J. Convex Anal.
25 (2018), 319-337.
20.
J.B. Kennedy
A toy Neumann analogue of the nodal line conjecture
Arch. Math. (Basel)
110 (2018), 261-271.
19.
J.P. Dias and
P. Freitas
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.
18.
P. Freitas
Sharp bounds for the modulus and phase of
Hankel functions with applications to Jaeger integrals
Math. Comp.
87 (2018), 289-308.
17.
O. Rouby
Berezin-Toeplitz quantization and complex Weyl quantization of the torus T2.
Portugaliae. Math.
74 (2017), 315-354.
16.
P.R.S. Antunes
Harmonic configurations of non-homogeneous membranes
Acta Acust united Ac
103 (2017), 596-606
15.
P.R.S. Antunes,
P. Freitas and D.
Krejčiřík
Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
Adv. Calc. Var.
10 (2017), 357-379
14.
D. Borisov and
P. Freitas
The spectrum of geodesic balls on spherically symmetric manifolds
Comm. Anal. Geom.
25 (2017), 507-544.
13.
G. Berkolaiko, J.B. Kennedy P. Kurasov and D. Mugnolo,
Edge connectivity and the spectral gap of combinatorial and quantum graphs
J. Phys. A: Math. Theor.
50 (2017), 365201 (29pp)
12.
P. Freitas and J. Lipovský
Eigenvalue asymptotics for the damped wave equation on metric graphs
J. DIfferential Eq.
263 (2017), 2780-2811.
11.
P.R.S. Antunes and E. Oudet
Numerical minimization of Dirichlet-Laplacian eigenvalues of four-dimensional geometries
SIAM J. Sci. Computing
39 (2017), 8508-8521.
10.
P.R.S. Antunes and E. Oudet
Numerical results for extremal problem for eigenvalues of the Laplacian
in Shape optimization and spectral theory,
2017, 398-411, Antoine Henrot (ed.), De Gruyter.
9.
D. Bucur, P. Freitas and J.B. Kennedy
The Robin problem
in Shape optimization and spectral theory,
2017, 78-119, Antoine Henrot (ed.), De Gruyter.
8.
P. Freitas and D.
Krejčiřík
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.
7.
P.R.S. Antunes
Is it possible to tune a drum?
J. Comput. Physics
338 (2017), 91-106.
6.
P.R.S. Antunes, C. Barbarosie and A.M. Toader,
Detection of holes in an elastic body based on eigenvalues and traces of eigenmode
J. Comput. Physics
333 (2017), 352-368.
5.
P. Freitas
Asymptotic behaviour of extremal averages of Laplacian eigenvalues
J. Stat. Phys.
167 (2017), 1511-1518.
4.
P.R.S. Antunes and R.A.C. Ferreira
Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
Commun. Nonlinear Sci. Numer. Simulat.
48 (2017), 398-413.
3.
N. C. Dias, C. Jorge and
J. Prata
One-dimensional Schrödinger operators with singular potentials: A Schwartz distributional formulation
J. Differential Eq.
260 (2016), 6548-6580.
2.
P.R.S. Antunes
Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain
Inverse Prob.
32 (2016), 115003.
1.
P. Freitas and J.B. Kennedy
Summation formula inequalities for eigenvalues of Schrödinger
operators
J. Spectral Theory
6 (2016), 483-503.