dr hab. Panayotis Smyrnelis
Παναγιώτης Σμυρνέλης
Assistant Professor at the University of Athens
Habilitation to supervise research from the Polish Academy of Sciences
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In 2013, in the Department of Mathematics with a cosmonaut, and in 2022, at a restaurant

Areas of interest

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

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

Research Articles

Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system
(with M. Kowalczyk and X. Lamy)
Archive for Rational Mechanics and Analysis 245 No. 1 pp. 565–586 (2022)

Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
(with J. Jendrej)
Applied Mathematics Letters 124 (2022) 107681

A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
Indiana Univ. Math. J. 70 No. 5 pp. 1745–1768 (2021)

Double layered solutions to the extended Fisher-Kolmogorov P.D.E.
Nonlinear Differ. Equ. 28 :48 (2021)

Vortex filament solutions in the Ginzburg-Landau-Painlevé theory of phase transition
Journal de Mathématiques Pures et Appliquées 156 (2021) pp. 328–350

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) Annali della Scuola normale superiore di Pisa,
Classe di scienze, Vol. XXI , issue special (2020) pp. 977–998

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

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.