Panayotis Smyrnelis

Παναγιώτης Σμυρνέλης

Assistant Professor at the Institute of Mathematics of the Polish Academy of Sciences

Researcher at the Basque Center for Applied Mathematics

E-mail address:

In 2013, in the Department of Mathematics with a cosmonaut

In the Department 
of Mathematics with a cosmonaut

Previous positions

Areas of interest

Elliptic systems of PDEs, Nonlinear ODEs, Calculus of Variations, Harmonic maps, Applications in Physics (nonlinear optics, liquid crystals, superconductivity)


Double layered solutions to the extended Fisher-Kolmogorov P.D.E.

Vortex solutions in the Ginzburg-Landau-Painlevé theory of phase transition

Connecting orbits in Hilbert spaces and applications to P.D.E.
Communications on Pure and Applied Analysis 19 No. 5 (May 2020) pp. 2797–2818

On the origin of the optical vortex lattices in nematic liquid crystal light valve
(with E. Calisto, M. G. Clerc and M. Kowalczyk)
Optics Letters 44 No. 12 (2019) pp. 2947–2950.

Gradient theory of domain walls in thin, nematic liquid crystals films
(with M. G. Clerc and M. Kowalczyk)
Communications in Contemporary Mathematics. 22 No. 7 (2020) 1950063 (27 pages)

The connecting solution of the Painlevé phase transition model
(with M. G. Clerc and M. Kowalczyk)
To appear in Annali della Scuola normale superiore di Pisa, Classe di scienze.

Minimal heteroclinics for a class of fourth order O.D.E. systems
Nonlinear Analysis, 173 (2018) pp. 154–163

Elliptic systems of phase transition type
Monograph with N. D. Alikakos and G. Fusco.
Progress in Nonlinear Differential Equations and their Applications, Vol. 91 Springer-Birkhäuser (2018).

Symmetry breaking and restoration in the Ginzburg-Landau model of nematic liquid crystals
(with M. G. Clerc and M. Kowalczyk)
Journal of Nonlinear Science (2018)

On Abrikosov lattice solutions of the Ginzburg-Landau equations
(with I. Chenn and I. M. Sigal)
Mathematical Physics, Analysis and Geometry. 21:7 (2018)

Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation
(with M. G. Clerc, J. D. Dávila, M. Kowalczyk, and E. Vidal-Henriquez)
Calc. Var. 56:93 (2017)

On minimizers of the Hamiltonian system u'' = ∇W(u), and on the existence of heteroclinic, homoclinic and periodic orbits
(with P. Antonopoulos)
Indiana University Mathematics Journal 65 No. 5 (2016) pp. 1503–1524.

A maximum principle for the system Δu − ∇W(u) = 0
(with P. Antonopoulos)
C. R. Acad. Sci. Paris, Ser. I 354 (2016) pp. 595–600.

Gradient estimates for semilinear elliptic systems and other related results
Proceedings of the Royal Society of Edinburgh 145A (2015) pp. 1313–1330.

Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures
(with P. Bates and G. Fusco)
Archive for Rational Mechanics and Analysis 225 No. 2 pp. 685–715 (2017).

Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry
(with P. Bates and G. Fusco)
Advanced Nonlinear Studies 13 No. 1 (2013) pp. 1–11.

The harmonic map problem with mixed boundary conditions
Proceedings of the American Mathematical Society 143 No. 3 (2015) pp. 1299–1313.

Existence of lattice solutions to semilinear elliptic systems with periodic potential
(with N. D. Alikakos)
Electron. J. Diff. Equations 2012 No. 15 (2012) pp. 1–15.


January 2020, Basque Center for Applied Mathematics

PhD course: Connecting solutions in second order phase transition models

Spring 2016, University of Chile

Fourier Analysis: undergraduate course (with Prof. M. Kowalczyk)

Spring 2015, University of Athens

Multivariable Calculus: undergraduate course (with Prof. L. Dalla)

Απειροστικός Λογισμός III - Τύποι του Taylor και Ακρότατα

Μάθημα 1, Μάθημα 2, Μάθημα 3, Μάθημα 4

Spring 2014, University of Athens

Methods of Applied Mathematics ΙΙ: postgraduate course (with Dr K. Liaskos)

Winter 2013-2014, University of Athens

EM.14 Nonlinear Analysis and Calculus of Variations: postgraduate course (with Prof. N. D. Alikakos)

Visits to Foreign Universities

  • July 15–August 23, 2020, visit to the University Sorbonne Paris Nord, France (upon invitation of Dr. Jacek Jendrej)

  • August 15–29, 2019, visit to the University of Chile, Chile (upon invitation of Prof. Michał Kowalczyk)

  • April 7–12, 2019, visit to the Basque Center for Applied Mathematics, Spain (upon invitation of Prof. Arghir Zarnescu)

  • April 26–May 1, 2014, visit to the Michigan State University, U.S.A. (upon invitation of Prof. Peter Bates)

  • October 19–November 4, 2012, visit to the University of Minnesota, U.S.A. (upon invitation of Prof. Peter Bates)

  • May 13–June 3, 2012, visit to the University of L'Aquila, Italy (upon invitation of Prof. Giorgio Fusco)

    The weather in Athens